it's a one-time shot though. You see what suggestions the LLM is producing, and decide or not to apply them. Once the code is refactored, you get back to regular coding.

That doesn't sound like it's less work than an "AI free" approach. The tricky part with refactoring isn't figuring out what needs to be changed and how, but to implement the change in a way that it works with the rest of the system, while at the same time actually improving things (and not just applying a different coding style).