I read the nice summary and that all seems reasonable to expect before being able to even remotely imply these things have any value as a mental health supporting tool.
AI therapists seem like a bad idea as a gut feeling to me, to be honest.
But thinking on it beyond my gut feeling, I recalled how my parents reacted 25 years ago when I told my them I was struggling with suicidal depression and pointed to an advertisement for prozac that described the things things I was going through.
My dad told me about how the advertisers were just trying to make a buck, and the doctors were paid to prescribe things and didn't care about my health, then my mom secretly behind his back put me on echinacea supplements.
In comparison it's hard to imagine an AI doing worse than that.
So gut feeling or no, and potentially pitfalls or no, this could be a tool to help people who can't otherwise get that help, and that has me hopeful.