I don't see what value the LLM would add - writing itself isn't that hard. Thinking is hard, and outsourcing that to an LLM is what people dislike.
Using an LLM to ask you questions about what you wrote can help you explore assumptions you are making about the reader, and can help you find what might be better written another way, or elaborated upon.
I'd push back a bit on "writing itself isn't that hard." Clear writing is difficult, and many people with good ideas struggle to communicate them effectively. An LLM can help bridge that gap.
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.