The task of helping to find wording that conveys your thoughts could mean several methods. It could mean you one-shot reword prompts and that helps you find wording. Or it could mean you're taking its output more substantially. Or you're going back and forth where the LLM is suggesting and you're suggesting too. It's incredibly vague what portion of "helping" the LLM is doing!

Whereas "search" implies (to me) a kind of direct and analytical process of listing and throwing out brainstormed suggestions, like you would with a search engine.

When I read the human version I actually get a sense of what that process looks like, and the LLM response definitely clouds or changes it by focusing on the result instead.

It is

The problem is that this becomes a race to the bottom of actual quality and turns into advertising.

Sponsored reviews of products are basically this. If you are paying a reviewer for a stamp of approval and the reviewer sets the bar too high, why would you want to pay that reviewer? On the other end of the reviewer, it's easy to get more money by providing that stamp of approval to more people--not fewer--so they're incentivized to make it fairly easy to achieve.