My background: for 8 years, I was married to a doctoral-level clinical psychologist with an active practice. I learned a lot about the industry from her. I've also seen many different therapists over my lifetime. Finally, I've the great fortune to have discovered a wonderful therapist almost a year ago. This was not my first wonderful therapist. But I've also had a number of poor matches over the years.
> it’s obvious they have an ethical responsibility to catch bad therapist/client fits
I can't really answer why they never come out and say, "I don't think I can help you as effectively as someone else." I don't really know. They just don't. I'm sure if you ask enough therapists, you'll get the odd exception here and there, like a therapist not comfortable with a client's erotic transference who then lets the client go. I don't know.
> Why should we not expect the therapist to catch scenarios of bad fit?
Perhaps they don't have the perspective. Perhaps they are trained to think they can help everyone, to some degree or another, and perhaps that's generally true. I don't know. But like finding a teacher who resonates with you, you won't learn the material as well or progress as fast unless the two of your resonate.
> Is the reason that I perceive a market for lemons simply that therapists’ profit motive is a moral hazard?
I don't think the majority of therapists go into their field for the money. I think there are lemons because of lack of experience and the highly-personalized experience; one person's lemon is another person's diamond.
I can't answer your other questions. I just want to emphasize that you need to advocate for yourself. If you don't feel like the therapist is helping you after 3 sessions, move on. Yes, you should have some progress after 3 sessions in my opinion. Doesn't have to be earth-shattering but should be something.
Re-read my above comment because I edited it several times after your post, adding more info (e.g. info about insurance)
Try not to Zoom your appointments. Go in-person!