It's valuable for you, the person who's going to spend a bunch of deep design effort, to make POCs. Is it valuable for someone else to drive by, dump some POCs on your lap, and then leave you to do the deep design effort while they run away to study AI?
If that person then runs around telling people that they're the real author of your project, because they generated the original POC, would you consider that an accurate assessment?
Your analogy is far enough away from the way that the real world works that I'm not sure that I can really even strain my experiences to fit within it. Sure, I guess that would be annoying?
But mathematicians define their field. They're smart people. They're capable of recognizing when someone just did a vibecoded throwaway PoC and when someone has a well structured proof. Actually even before LLMs they'd publish new, clearer or more elegant proofs of old results. They can say that inscrutable proofs are exactly as valuable as they are, and that the first explanation people can actually understand carries its own prestige.