I work in psychiatry and can say that the ELiza effect is definitely real. There is a concept of 'deference' which people tend to ascribe to people in authority especially doctors and psychotherapists. Its a way of absolving yourself of responsibility to be guided by some expert - emotionally, a bit like taking the world off your shoulders.

Over in the UK we have a homeopathic hospital. Its just like a real hospital and it has the same smells corridors. waiting rooms, uniforms everything like that. The only thing about it is that all the medication it uses is homeopathic and as every rational person knows is completely ineffective in terms of sceintific analysis (OK you can disagree but thats a scietific view)
The 'patients' of this hospital show the same amount of deference as would be ascribed to a genuine medical Dr and the 'Drs' of homeopathy have the same body language and forms of intervention as conventional Drs. If there is a beneficial effect its (IMO) a form of placebo effect.

Working thirty years in the profession running wards in hospitals you get SOME Drs whose decisions could be potentially disastorous or even lethal to patients, that are kept in line by the nurses that work for them. There knowledsge is poor to non existant, to the extent that you might even suspect that their qualifications are not genuine, but, and this is my point, they get the same deference and respect from the patient because the patient gives this trust as an article of faith rather that because it is verified. The patient leaves the verification to other parties.

Win 11 64, Asus Rog Strix z390 mobo, 64 gig RAM, 8700k