Why are the financial intermediation theory of banking or fractional reserve theory of banking still accepted despite evidence to the contrary? In most textbook economics I came across the financial intermediation theory of banking and the fractional reserve theory of banking are presented as theories as how money is created.
However there is evidence that these theories are wrong. See for example
Economist A. Werner writes in his empirical case study:

An empirical test is conducted, whereby money is borrowed from a
cooperating bank, while its internal records are being monitored, to
establish whether in the process of making the loan available to the
borrower, the bank transfers these funds from other accounts within or
outside the bank, or whether they are newly created. This study
establishes for the first time empirically that banks individually
create money out of nothing. The money supply is created as ‘fairy
dust’ produced by the banks individually, &quot;out of thin air&quot;.

The study even includes a letter signed by the manager of the bank in which Werner did his experiments:

Dear Prof. Dr. Werner,


Confirmation of Facts


In connection with the extension of credit to you in August 2014 I am pleased to confirm that neither I as director of Raiffeisenbank Wildenberg eG, nor our staff checked either before or during the granting of the loan to you, whether we keep sufficient funds with our central bank, DZ Bank AG, or the Bundesbank. We also did not engage in any such related transaction, nor did we undertake any transfers or account bookings in order to finance the credit balance in your account. Therefore we did not engage in any checks or transactions in order to provide liquidity.


Yours sincerely,


M. Rebl,


Director, Raiffeisenbank Wildenberg e.G.

Similar claims are made by Kumhof and Jakab published by the IMF (International Monetary Fund):

Specifically, virtually all recent mainstream neoclassical economic research is based on the highly misleading “intermediation of loanable funds” description of banking, which dates to the 1950s and 1960s and back to the 19th century.We argue instead for the “financing through money creation” description, which is consistent with the 1930s view of economists associated with the Chicago School. These two views have radically different implications for a country’s macroeconomic response to financial and other shocks. This in turn has obvious relevance for key policy choices today.­
Lending, in this narrative, starts with banks collecting deposits of previously saved real resources (perishable consumer goods, consumer durables, machines and equipment, etc.) from savers and ends with the lending of those same real resources to borrowers. But such institutions simply do not exist in the real world.
There are several reason for it. Please note the reasons are not necessarily listed in order of importance, the last point is actually most relevant answer to your question.

The 'Evidence' You Cite is Controversial

First, in fact the work you cite itself states that this issue is matter of ongoing controversy (Werner, 2014). So it is far from settled.
However, what even more the empirical 'test' of Werner (2014) is itself actually quite controversial and has been criticized heavily  for confusing accounting with economics (e.g. see Rendahl &amp; Freund 2019 or Spearman 2016).  Accounting and economics are completely distinct disciplines so it is often not possible to conclusively test economic theory just by accounting arguments.
For example, a theory of perfect competition predicts that in equilibrium there will be no economic profit. However, you can't test whether firm has zero economic profit by looking at the firm's profit and loss statements because accounting does not capture economic reality and does not include things like opportunity cost which could make profit zero. Depreciation in accounting is also treated in a way that economically has almost no sense etc. As a result even if in real life there would be some perfectly competitive industry you cannot test for that just by looking at firm's profit and loss statement but you need better more nuanced test.
In a similar way the paper by Werner is criticized for making essentially the same error of assuming that just because on the balance sheet money seemingly appear out of nothing that means that banks actually can create them out of nothing, and as explained in greater detail in Rendahl &amp; Freund (2019), that is to a degree just accounting fiction and does not really prove that banks do not create money against some assets as understood in economics (as opposed to what accounting understands them to be - which again is completely separate discipline with its own terminology and very little relation to economics).
Next, when it comes to financial intermediation, it would again be quite controversial to state that banks do not engage in some financial intermediation. Even McLeay et. al. (2014) argue financial intermediation plays some role in money creation. Now this is not the same as claiming the authors endorse financial intermediation theory the point is that stating that banks do not engage in financial intermediation at all would be controversial.
Textbooks are generally not being rewritten if one controversial paper is published. It takes time for literature to settle. Even if the new controversial paper is entirely correct it can take few years before that is reflected in textbooks (especially undergraduate ones graduate textbooks are much more up to date).

All Models are Wrong but Some are Useful (George Box)

As the title of this section says all models are wrong, you can imagine model as being a map. Any map that is not 1:1 replica of landscape will be wrong in some way, however having 1:1 replica of landscape as a map ceases to be model and quite frankly it is completely useless even though it is 100% correct. Both 'fractional reserve theory' and 'financial intermediation theory' have their utility.
Starting with 'fractional reserve theory'.  For example, before 2009 when central banks started engaging in 'unconventional' monetary policy,  the 'fractional reserve theory' was quite useful for back of the envelope calculations. This is because pre-2008 commercial banks held virtually no excess reserves as you can see from the data provided by FRED below:

In such situation, the 'fractional reserve theory' can be actually quite useful and reasonable approximation. As you can see from graphs below, the $M_2/M_1$ ratio and amount of reserves before 2008 tended to move in same direction.


In fact if you remove observations post 2007 and calculate correlation between $M_2/M_1$ and required reserves you would find the correlation to be significant with point estimate approximately  $0.55$ (with $95\%$ conf.  interval (rounded to 2 significant digits) $[0.49, 0.60]$)*. Sure simple correlation is no rigorous test, but with such high correlation it is difficult to claim that there is no relationship between reserves and ratio of $M_2/M_1$ meaning that at least in past money were created in a way that looks like a situation where banks just multiplied reserves (again I am not saying this is necessary rigorous test, one can invoke reverse causality and so on,  point is that its not an unreasonable model for a first approximation).
Now for sure utility of the 'fractional reserve theory' diminishes greatly under the new unconventional monetary policy, and especially now that many central banks around the world (but not all) completely abolished reserve requirement altogether (see Fed explainer on its abolishment of reserve requirements here). However, it is not clear if this is new normal. These policies are still referred to in the literature as 'unconventional' and  it is not clear if they will last. In fact before the Covid-19 hit world economy, Fed was already contemplating of returning to normal policies (e.g. see news articles pre-Covid such as this one). Consequently, an argument can be made that this model is useful for students to understand because it described banking relatively (relative to its simplicity) well in the past, and it is not so clear if the current unconventional monetary policies that make the model give very wrong predictions will last.  You should also note, that it is not like this is the only model textbooks discuss. For example, Blanchard et al Macroeconomics: A European Perspective pp 71 described failures of simple multiplier model and alternative endogenous money supply theories already in 2013.
When it comes to 'financial intermediation of banking' theory this one has still its uses even contemporary empirical research (See discussion in Freixas &amp; Rochet Microeconomics of Banking). Consequently, when it comes to this theory it is even more useful for students to know, even if you can of course criticize it and competing theories exist.

Both Theories are Important for Didactic Reason

Since we are discussing textbooks and not applied research it is important to realize that textbooks, beyond anything else, serve didactic purpose. They are intended to be used as teaching tool, and especially undergraduate textbooks (which is where you will see 'fractional reserve theory' and 'financial intermediation theory' given most space) have to build foundations for future study.
For example, every single intro physics textbook in existence will teach Newtonian physics, even though we now know that Newtonian physics is wrong and at best special case of general relativity. Yet learning incorrect Newtonian physics is still useful as it can be used for back of the envelope calculation in many situations  and it will still give reasonably good answers. As shown under point 2 even simple 'fractional reserve theory' provides quite reasonable predictions (although it is definitely not as close as Newtonian theory to general relativity so please do not take this analogy too far).
This is like asking why textbooks typically include linear demand and supply when in reality demand and supply is almost never linear. Well answer is that solving models with simple linear demand and supply is easy for students and facilitates learning, as it serves as a stepping stone to understanding more complex models. For example, in typical graduate microeconomic textbook you will virtually never see linear demand or supply save for some rare exceptions, yet if you would try to teach 101 econ students from graduate textbooks such as MWG Microeconomic Theory or Varian Microeconomic Analysis, all but the top $5\%$ of class would fail miserably.  Again you would end up in analogous situation if you would start physics 101 with  Einstein's  field equations. Anyone except for top students would not be able to follow. As a result you will fail in your task to educate students, since even students that might become excellent physicist when they learn physics in small steps instead of trying to directly tackle graduate level physics, would never be able to achieve their full potential if you would just stress teaching more realistic but infinitely more complex models. Again this does not mean such models should not be taught but there is plenty of room for that in graduate courses.
Even McLeay et al (2014) who very harshly criticize 'fractional reserve theory' argue it can be a

useful way of introducing money and banking in economic textbooks,

Next, it is also important to understand that both 'fractional reserve theory' and 'financial intermediation theory' are part of exogenous money supply theory (a theory where private banks are passive agents that just expand/contract money supply in a way that is exogenously dictated by central bank), and regardless whether you consider exogenous money supply theory right or wrong (I personally think exogenous money supply theory is far from completely correct), learning exogenous money supply theory is important part in learning endogenous moneys supply theory (which is theory where private banks have active role in money supply creation).
This is because as discussed earlier, even authors who are proponents of endogenous money supply theory such as McLeavy et al (2014), do not deny that banks are constrained by central bank's policy and that some financial intermediation is taking place.
The difference between exogenous money supply theory and endogenous money supply theory is that under exogenous money supply theory the chain of causality goes just from central bank policy to money supply, whereas under endogenous money supply theory there is relationship that goes both ways (see more details on this in above mentioned Blanchard et al). Consequently,  endogenous money supply models will still feature central banks policy be it via reserves or more often other ways that affect money supply like bank regulation/interest rates etc,  and will still often have banks that still take in deposits. Rather under endogenous money supply theory there will be additional relationships where money demand will cause banks to lend more and in turn banks will then create more reserves at the central bank (like described in McLeavy et al).
Consequently, even if you think exogenous money supply theory is completely wrong, it is didactically better to first teach exogenous money supply theory, and then explain to students that this is wrong because there are additional channels that lead to simultaneity/reverse causality and build your explanation of endogenous money supply theory based on exogenous money supply theory. Jumping directly to endogenous money supply theory would likely just facilitate less learning and create more confusion even if your goal is to teach only endogenous money supply theory.
The above alone is the most important reason why these models heavily feature and will likely continue to feature in most 101 macro textbooks in foreseeable future. However, you should note that the space most mainstream macro textbooks devote to exogenous money supply models has shirked substantially, you can verify that by comparing the latest editions of Mankiw Macroeconomics or Blanchard et al Macroeconomics to their earlier editions.   Nowadays, you will get quite more space devoted to endogenous money supply theories (however, do not confuse endogenous money supply theory with controversial assertions of Werner (2014) of money being created completely ex-Nihilo by private banks - that is very controversial compared to just general endogenous money supply theory).

* Code for the correlation calculation in the spoiler:

 #data are obtained from fred data linked above, data after 2007 are deleted, data were merged in excel before runing the code (with raw output below): 
 cor(fred$M2SL_M1SL, fred$REQRESNS, method = c(&quot;pearson&quot;)) 
 &gt; [1] 0.54867 
 cor.test(fred$M2SL_M1SL, fred$REQRESNS, method=c(&quot;pearson&quot;)) 
 &gt; Parson's product-moment correlation 
   data:  fred$M2SL_M1SL and fred$REQRESNS 
   t = 15.887, df = 586, p-value &lt; 2.2e-16 
  alternative hypothesis: true correlation is not equal to 0 
 95 percent confidence interval: 
  0.4895299 0.6027855