I don't think it's a useful substitute for actual proofreading though, unless you're truly in a time crunch. When I proofread I don't just look for mistakes, I try to put myself into the position of a prospective audience member. LLMs seem to have absolutely no concept of "theory of the reader's mind". If I'm going for extra high effort, I have friends read it, usually asking them to identify anything that was unclear or hard to follow.

As a "proof" of their poor judgement, take a paragraph you like. Ask the LLM to rewrite it to make it better (which I think we both agree will not make it better), and then in a fresh session ask it which it thinks is best. It'll almost always pick its own writing, even when it sucks.