You're just moving the problem around. Instead of OpenAI and Anthropic dumping proofs, you'd instead have someone (maybe an aspiring graduate student, maybe a hobbyist, maybe an established mathematician who has disdain for existing process) dump these proofs en masse personally.
Dumping the one proof they have access to, sticking their name next to “OpenAI” and having it preside over reams of incomprehensible slop? Instead of taking a few months to digest, improve, rework it? I mean, maybe a few would, but I don’t think this objection holds much water.