If OpenAI researchers are publishing shoddy papers, why in the world would anyone else be responsible for editing and cleaning up their shoddy papers?

No one is "responsible". If the paper is read, depends on the interest of the individual scientist. Many mathematicians interested in a theorem proven/disproven in a new AI paper will be curious, even if it is utterly cumbersome to extract the relevant line of thought. But don't you agree that the job can only be done by a mathematician anyway - be she/he paid by the company or by a university?!

What you are arguing for is somewhat like the "proprietary period" in astronomy (e.g. see https://www.scientificamerican.com/article/nasas-plan-to-mak... ). But there is no mathematician who asked for the run of AI, i.e. there is no mathematician, who can be regarded as the owner of the result, even if ownership was temporary. Complex proofs might take years to explain in detail (think of the ternary Goldbach problem, https://en.wikipedia.org/wiki/Goldbach%27s_weak_conjecture ). It's just unfair, if AI companies held back with their data until a proof has been put into a nicely readable article, and at the same time mathematicians elsewhere are spending all their time trying to solve it.

> which I am happy to pay with my taxes

I'm not. To the extent my taxes are used for maths research (which is minute as a proportion of them) I want them to be used for the development of human mathematical understanding, culture and education, not trawling through a mountain of slop mechanically generated by a Silicon Valley startup that's about to IPO for trillions in the hope there might be some nuggets of insight hiding in there. If the latter is an activity with some value the startup in question can pay for it.