All my points have already been (better) covered by others in the time it took me to type them, but instead of deleting will post anyway :)
If your concerns are about AI replacing therapists & psychologists why wouldn’t that same worry apply to literally anything else you might want to pursue? Ostensibly anything physical can already be automated so that would remove “blue-collar” trades and now that there’s significant progress into creative/“white-collar” sectors that would mean the end of everything else.
Why carve wood sculptures when a CNC machine can do it faster & better? Why learn to write poetry when there’s LLMs?
Even if there was a perfect recreation of their appearance and mannerisms, voice, smell, and all the rest – would a synthetic version of someone you love be equally as important to you? I suspect there will always be a place and need for authentic human experience/output even as technology constantly improves.
With therapy specifically there’s probably going to be elements that an AI can [semi-]uniquely deal with just because a person might not feel comfortable being completely candid with another human; I believe that’s what using puppets or animals or whatever to act as an intermediary are for. Supposedly even a really basic thing like ELIZA was able convince some people it was intelligent and they opened up to it and possibly found some relief from it, and there’s nothing in it close to what is currently possible with AI. I can envision a scenario in the future where a person just needs to vent and having a floating head just compassionately listen and offer suggestions will be enough; but I think most(?) people would prefer/need an actual human when the stakes are higher than that – otherwise the suicide hotlines would already just be pre-recorded positive affirmation messages.