How something is proven is often more important than what is being proven. There are underlying systems and patterns that, when understood properly, improve our model of mathematical (or physical) reality.

With convoluted and inelegant proofs, AI may fail to uncover those systems and patterns. As a most concrete example, it may fail to recognize some problems as isomorphic to other problems. Brute force solutions are a depth-first search.

To improve human mathematical understanding, AI is probably best used as a “copilot” (lol) rather than a black box oracle, like these AI companies appear to be doing.

I'm sorry this framing is just moving goal posts.

If you're after new methods. Then new methods is the goal, the answer to the question is not the goal then. The animated response indicates the answer wasn't just a byproduct.

There is still something to glean from the answer. You have a further constraint. Otherwise whatever "new method" proposed may as well be hallucination, potentially taking you in the wrong direction away from the answer.

This line of thought is not unique, stonemasons made obsolete by uniform brickword suddenly were "worried about the art and preserving traditions".