I've thought exactly that "writing is thinking" before as a reason to not let a LLM write for me.
Then again, I've seen a counterargument [1] by someone who clearly heavily uses LLMs for writing (going by both their LLMy writing style and their own admission). The person I'm citing describes a process where they get a LLM to write something, they check over it and provide feedback to the LLM, the LLM rewrites, and the process repeats iteratively. So clearly he is putting thought into the process.
I think there is something valuable missing, even if it's hard to clearly express. I'll try. The threshold for what I'm willing to accept if I'm simply approving something is likely different from what I'll get if I write something myself, for instance. Saying "LGTM" is too tempting. It seems to me like he's outsourcing his selection of topics to cover as well. If you're not thinking yourself about what to cover then it would be very easy to miss a critical subject. There also an asymmetry between checking and generating something with constraints placed on it. Checks can't catch everything, and a constrained generating process can reduce the amount that needs to be checked, avoid issues that can't be checked so easily, and focus your attention on areas that you know historically have had issues with this generating process. I've thought about this quite a bit in terms of whether to write new code or use an existing library. Sometimes "the devil you know" (my code) is better than an existing library simply because I understand its flaws better.
I've tried doing it that way, and thought it was even acceptable for the reasons you said. I did learn a lot through that process and clarified my ideas. But later I rewrote the whole thing from scratch and then had the LLM review it. It made some good suggestions but no substantial changes. The difference was night and day. That final product had my voice, and I understood it better. LLMs are powerful tools and can improve quite a lot of the writing process, but using them to do all the writing leaves a lot on table along with your fly open.