I have had two therapists (psychoanalysts) and although both of them have occasionally filled a parental role for me, I don't think they fulfilled their parental desires. Both of them have always kept in mind all my parts (adult, woman, mother etc) even at those times when I was presenting as a child and did not remember anything else in those moments. At the same time, they are the only persons I've experienced as motherly (my own mother failed utterly in this respect) although they both are men.

So, I don't know if therapists in general or many of them fulfil their parental desires with patients, I haven't experienced that but I would probably spot it and run from that kind of therapist as soon as possible.