Reading through docs and doing research: of course. They're like much better search engines in that regard. It would be silly not to use them. Obviously, you need to review their search results against their sources.

Structuring arguments: bad idea. Here you're having the model do your thinking for you. The problems that occur with having it write text recur at a macro level; too-obvious patterns. Readers just want to know what the prompt was.

Writing the prose: obviously not.

Proofreading: I think this works pretty great, as long as you have a structure to how you're doing it. "How do I make this better or sharper": bad, you're having the model structure your arguments for you. But for a predefined rubric of stylistic things --- writing you know how to do, that's just tedious to check manually? Hard to see a downside.