I do agree with your core point - the thinking is what matters. Where I've found LLMs most useful in my own writing is as a thinking tool, not a writing tool.
Using them to challenge my assumptions, point out gaps in my argument, or steelman the opposing view. The final prose is mine, but the thinking got sharper through the process.
Especially since everyone harps on about it but never provides concrete evidence. If your thinking has sharpened, surely you can find a way to demonstrate how.
I suspect it's one of those things where the user thinks they have improved but the reality is different.