"The real question is can they do a better job than no therapist. That's the option people face."
This is the right question.
The answer is most definitely no, LLMs are not set up to deal with the nuances of the human psyche. We're in real danger of LLM accidentally reinforcing dangerous lines of thinking. It's a matter of time till we get a "ChatGPT made me do it" headline.
Too many AI hype folks out there thinking that humans don't need humans, we are social creatures, even as introverts. Interacting with an LLM is like talking to an evil mirror.
Now, I don't think a person with chronic major depression or someone with schizophrenia is going to get what they need from ChatGPT, but those are extremes, when most people using ChatGPT have non-extreme problems. It's the same thing that the self-help industry has tried to address for decades. There are self-help books on all sorts of topics that one might see a therapist for - anxiety, grief, marriage difficulty - these are the kinds of things that ChatGPT can help with because it tends to give the same sort of advice.
"...for people lacking the wealth or living in areas with no access to decent housing, unmaintained dangerous apartment buildings are a godsend."
Why is it ok to expect poor people to be endangered and suffer through indignity just for the "crime" of being poor?