> they won't necessarily be much wiser about why those methods work, other than having a good intuition confirmed by numerical experiments.

This is the state of the field as a whole, isn't it?

> Wouldn't it be more useful to dedicate the space to convergence proofs for ADAM (which do exist)

Convergence proofs don't really explain why Adam tends to work better than other methods.

It's hard to blame them for not being able to explain things that, currently, nobody understands. But I guess it kind of undermines the idea of a theory-heavy approach to teaching if the theory we have can't predict the things that are actually important.