> “good” API design (highly subjective)
A good API does two things. Firstly it DRYs the code out. Many APIs start life doing only that, as a collection of routines you get tired of writing over and over again. Secondly, the functions are designed in a way that reduces the need to share information. Typically they do that by hiding a whole pile of details in their implementation so knowledge of those details is all in one place rather than scattered across a code base. A term often used for APIs that don't do that well is "leaky", or we say it's a "leaky abstraction".
Perhaps a good API has other more subjective attributes but it must have those two. LLMs suck at both. You can see that in the comments here, when people say they write verbose code. It's verbose because the LLM didn't go looking for duplicated functionality - if it needed it, it just put the code where it was focused on at the time.
If they are bad at DRY then I need a better superlative to describe how they fare at respecting the isolation boundaries that underpin good module design. As far as I can tell, they have no idea about the concept or how to implement it. Let loose, they are like a bull in a china shop, breaking one boundary after another.