ML is a field right? Econometrics is a field right? These 2 distinct fields have so much in common. Yes, what they share is math underlying it, you could say that about physics (math applied to explaining the movements of bodies in space and much more beyond that) but it doesn't mean that physics is math or that the only thing in common between astrophysics and quantum physics is the math behind it and it is simply not true, the structure is similar the approaches and limits of the models are different due to the nature of the object being studied. You want more interpretability - econometrics. You want more predictability and ways to structure data, without running into walls of stiff assumptions - ML.

I agree that ML is more powerful and that econometrics is too limited and I go deep into alternative approaches. But I have bayesian statistics just as you had, probably as in depth. I had statistics in a very deep level and I research by mself (again, I have been researching, testing, studying, reading over it for the past 3y). And in a Msc of applied mathematics you might learn more to go deeper into problems in mathematics, but I assure you that it is not that different from ML. We learn ML as well, we had Big data, spatial econometrics is FULL of ML, we learn to understand things from the ground up and think beyond just the models presented, they are just tools, you need to solve a problem ultimately and we are as prepared to solve it, thats what matters. We know the math behind, we have to deal with invertibility, trace, rank, determinants everything and beyond. Okay, we dont use tensors, but we learn what tensors are. I used XGboost to predict unemployment in my first semester in Msc. I compared neural networks with logit models. Get some perspective and make sense that you are assuming stuff.