The relation between econometrics and machine learning In my understanding the utility of econometrics versus machine learning is generally argued to be the research of causality.
If I'm not wrong, when we put aside experimental economics, the golden standard to prove causality is to use Intrumental Variables. But in practice it has been showed that finding a relevant IV is often not possible, and authors end up taking the best &quot;IV&quot; they can find.
Problem: This variable has a high chance to not in fact be exogenous, but we can not verify it when the IV is dependant of variables like happiness, for example. Since we have no way do verify those dependances, science stops here.
SO I am wrong to say that in most cases econometrics can not scientifically establish causality? In that case why using traditional econometrics instead of modern machine learning techniques?
I.)  2 Principles of econometrics can potentially be useful compared to Machine Learning.
(see  Hal R Varian 2014 Paper : https://pubs.aeaweb.org/doi/pdf/10.1257/jep.28.2.3)

A.) As you suggest the search of causality is one advantage but unlike what you think, even if causality sometimes could be tricky to measure it remains very useful and functional.

But first,  when you suggest that Instrumental variable is the only available tool which work for most of the cases and allow causal inference, i think there is a few more techniques that could  still be applicable  to measure causality in response to a treatment, a manipulation, or an intervention and still be relevant (unlike natural experiment as you precise because of its restricted direct applicability to most of the cases) in most of the situations such as:

● explicit experiments
● regression discontinuity
● difference in differences
● structural estimation

For instance you can investigate causality with theses techniques or instrumental variables because even if those techniques are subject to bias and correlation issues (all the more since big data because the increasing size of datasets limits the usefulness of instrumental variable methods, depending on instrument strength and level of confounding), it still give a hint to investigate causality. 
In a way that, for instance, it enables the detection of conditional counterfactual (an if-clause which is contrary to fact) while also check the existence of potential selection bias.

What is a Conditional counterfactual:

If it is raining, then he is inside.  : Rain = Indicative Variable 

If it were raining, then he would be inside. : Rain = Conditional Counterfactual variable 

Hence, the better predictive model you have for the counterfactual, the better you will be able to estimate the causal effect.
Thus, even though a predictive model will not necessarily allow one to conclude anything about causality by itself, such models may help in estimating the causal impact of an intervention when it occurs.
Because it can highlights a bunch of conditional counterfactual which could be use as potential causal Variables to run the test on, in order to  eventually determined causality in a given dataset to do good decision making (clean up from confounding issues). If not, at least, it gives you some clues to conduct a deeper investigation to understand the problem : anything wrong with the theory ? anything wrong with my econometric model ? anything wrong with my data ?.

For more insight about the pro cons of differents causal inferences techniques in econometrics : 

https://www.jstor.org/stable/pdf/44234997.pdf?refreqid=excelsior%3A18bacfd86299dcf19e7f1f13d9c52022

B.) Except causality, model uncertainty is another advantage of Econometrics compared to ML.

Probabilistic foundation of econometrics is a strenght in a way that it allows interpretability of most of the models and their parameters (avoiding black box phenomenon) and give a quantisation of uncertainty (with confident intervals ) .
The goal is usually to show that the estimate of some interesting parameter is not very sensitive to the exact specification used : how an estimated parameter varies as different models are used.This question illustrate a simple form of model uncertainty.
In this period of “big data,” it seems strange to focus on sampling uncertainty, which tends to be small with large datasets, while completely ignoring model uncertainty, which may be quite large. 
One way to address this is to be explicit about examining how parameter estimates vary with respect to choices of control variables and instruments.

II.) On the contrary Machine Learning techniques could  also be useful for data analytics in social Science.

A.) Parameters Selection, Model validation methods in ML can improve traditional econometrics models

Researchers in machine learning have developed ways to deal with large datasets and economists interested in dealing with such data would be well advised to invest in learning these techniques.
For instance, Web Mining methods could discover new usuable explanatory variable.
Cross validation should identify a non-linear effect or a forgotten cross effect. 
Model Validation should detect when a model is mispecified and thus allows a better specification of an econometric model and on the whole reduce omitted variable bias and error.
As an example, recent litterature in finance focus on Garch models (traditional times series models) improved with Neural Network to better predict volatility and asset prices.

For more insight about the usefulness of ML in econometrics check out this paper by Arthur Charpentier : https://arxiv.org/pdf/1708.06992.pdf

B.) Causal Modelling began to be a concern and a field of research in ML. Which means that in the long run ML could potentially overcome its own flaws ( like being exclusively focus on the fit ) and outperform Econometrics.

Some Theoretical computer scientists, such as Pearl (2009a, b) have
made significant contributions to causal modelling in computer science (by extension machine learning):

(see:  Causal Inference in Statistics: A Primer Wiley, 2016  Judea Pearl et Al)

Pearl defines counterfactuals directly in terms of a "structural equation model" – a set of equations, in which each variable is assigned a value that is an explicit function of other variables in the system. Given such a model, the sentence "Y would be y had X been x" (formally, X = x > Y = y ) is defined as the assertion: If we replace the equation currently determining X with a constant X = x, and solve the set of equations for variable Y, the solution obtained will be Y = y. This definition has been shown to be compatible with the axioms of possible world semantics and forms the basis for causal inference in the natural and social sciences, since each structural equation in those domains corresponds to a familiar causal mechanism that can be meaningfully reasoned about by investigators.

However, it appears that these theoretical advances have not as yet been incorporated into machine learning practice. Except in some recent research paper :

http://www.nasonline.org/programs/sackler-colloquia/documents/athey.pdf

As a Conclusion, in my opinion and as things now stand, Econometrics as more valuable input in social science than what machine learning could bring. So it is still adequate to use econometrics to conduct data analysis instead of ML techniques.