Measuring demand for banking services - (Maximum) Market Size I am in need of a variable measuring "demand for banking services" in general, on a country level. Specifically the (maximum) size of the market for banking services for a given country. This will be used as a control variable.

Does anyone know any standard proxies or measures used in the literature to measure something like "total demand for banks"? I need something general, not a specific banking service. Something that summarizes the different sources of demand for banking services, such as some kind of constructed index or so. Something that summarizes everything/most services through which banks make profits. If that is not possible, are there maybe two standard measures that each cover demand for deposits and demand for loans? 

What variables are generally used? If nobody knows what is standard, does anyone have any plausible suggestions of proxies/measures for "demand for banking services"? Further, any suggestions on data sources I could use to get country level data (preferably a panel starting around the '80s or '90s) for such a variable?

The proxy/measure need not be perfect. The only important thing is that it captures "the size of the market for banking services (in general)" in some way. Especially a measure of demand that would determine the (maximum) number of banks in a given country.
There is no quantifiable answer as the concept is illusory.  Banks operate by mismatching short term debt with long term assets.  This has no benefit to the economy as a whole and in fact creates inflation, risk and volitionality.  Banks operate maturity mismatching because they can and it serves their own interest.  There is no natural demand for banks which is why they are in need of constant artificial support from central banks (much of which happens on a daily basis).  Without central bank support, banks would be accountable for mismatching short term debt with long term assets and they would quickly and rightly so burn up in a liquidity fire.

Perhaps a better premise to start before mathematically quantifying the demand for banks is to ask conceptually the role banks play in an economy first.  Without conceptual and contextual understanding, math is meaningless number juggling designed to impress and confuse those that don't know better.

Now...it can be said it said there is a demand for money of which banks create.  Imagine if we were to switch to the gold standard all of sudden.  Only gold could be exchanged for services.  Because gold is limited, the price for it (to acquire as a means of exchange) would shoot up astronomically.  This profiting (from gold sellers to gold buyers) represents economic loss for the buyers.  If they could acquire another means of exchange (say gold deposits that were not tied 100% to gold) they would not have to pay as much for the gold.  So in a way banks can create competition for money.  But in doing so they create either their own inflation or profiteering.  Then there is of course the matter of fiat currencies competing which never ends well...

Personally, that is why I'm in favor of a national depository that would negate the need for deposit banking.