Yes, but when a therapist starts bringing his or her own self--emotions, reactions, etc., into the therapy, it turns into something that is no longer therapy. The key word being reactions because I think reciprocity you are suggestion invites reactions. Perhaps you can't have all the good elements of a relationship without the bad (e.g. reactions).

I think it's the opposite--reciprocating the same as in any other relationship can be damaging or harmful. But it doesn't have to be either or. A therapist who discloses nothing can prevent trust from building in the relationship. Relational psychoanalysis is one where the therapist is spontaneous and genuine at times. But, someone in training to be a psychoanalyst spends years in intense therapy. By the time they are done, all of their transferences are worked through, enabling them to separate their feelings from those of the client. This prevents the reactivity I see happen so much here. (not that this training makes them completely immune from this).

Therapists who did not have years of their own depth therapy, I would argue, are unlikely to be able to do this and risk harming the client.

Edited to add: its the therapist's needs entering the therapy that is most problematic. Reactions being just one example of the expression of a need. The reciprocity you suggest comes with needs.