Everyone anti-AI I know (which is most of everyone I know who's cognizant of AI) would respond by either finding a therapist who can promise they won't do that, or else not get therapy at all.

LLMs are not worth trusting for basically anything, and a lot of fields are quickly realizing this. I keep my finger on the pulse of programming and there's a lot of negative sentiment there too—I've never used LLMs to code and I never will, but I know of a few folks who've explicitly said how much it screws things up, and I've seen studies that found it to be seriously lacking at best.