I've played with a similar idea for writing technical papers. I'll give an LLM my draft and ask it to explain back to me what a section means, or otherwise quiz it about things in the draft.

I've found that LLMs can be kind of dumb about understanding things, and are particularly bad at reading between the lines for anything subtle. In this aspect, I find they make good proxies for inattentive anonymous reviewers, and so will try to revise my text until even the LLM can grasp the key points that I'm trying to make.