That's precisely the reason why I think that putting a fancy name to certain qualities in healing human relationships is problematic. As evident in this thread, the word 'reparenting' itself creates a sense that someone is going to force something unwanted and inappropriate down one's throat whereas it is absolutely not the case. I don't think for something that can be gathered under the term "re-parenting" necessarily assumes the T having authority over the patient. At the same time, I don't see that it can be substantially reciprocal because the participants in therapy have clear roles - one is in need of help and the other one is providing that. But I absolutely agree that performing these functions is not exclusively the role of the therapist - other people can do that too.

Also, this "attachment therapy" thing is according to my knowledge not really a thing anymore. What people consider as "limited reparenting" in schema therapy has nothing to do with these outrageously infantilizing activities adopted by some therapists in 70s and 80s (and perhaps also 90s). I'm pretty sure that noone who claims to cultivate this type of therapy nowadays is able to keep their professional license. Thus, the meaning of the "reparenting" in therapy really refers to the methods used in schema therapy and thus to just a lot of sensible things that therapists do with their long term patients according to the patient's needs, and not the literal activities as meant in the context of this historical "attachment therapy".

The main reason I personally would prefer not to give these things the name "reparenting" is precisely although some people would need these functions to be performed to them by their therapist (emotion co-regulation, boundary setting, whatever), the term might sound infantilazing to the person although the particular functions, if tailored to the patient's needs, clearly aren't.