[ineedasername]

>If your goal is become a better programmer, your time is better spent working on challenging programming problems.

I disagree. If the you'd answered an aspiring engineer with "your time is better spent on challenging engineering problems" then, at the level the asker of this questions seems to be at, that would not be the best advice. A person could bootstrap their ability much faster by studying first (or concurrently) other subjects as well.

I think the same applies to programming. I don't have a strong opinion on proof-based math in particular but "just do $skill" is a large oversimplification glossing over the fact that most skills require at least some subject matter knowledge that is a precursor to performing the skill, either because it's necessary in itself or because studying the subject instills some transferable skills as well.

In the case of proof based math, one skill you learn is how to begin things, or break them down, to first principles and build up from there. That's extremely useful for programming, or problem solving in general. You can learn it in different ways, not just from math, but learning it through math or some other subjects are much more direct paths to obtaining that skill, if you don't already have it, than jumping only into programming.