I don't see the "broken" view as at the heart of psychotherapy's history. I think Freud mostly discounted the notion of "person" almost entirely; the focus was on the mind, almost as a disembodied entity, with no respect for what we would now call the socio-cultural aspects of personhood. I believe that was part of what Rogers was reacting against.

I think this sense of therapy as a reflection of social dynamics, including power structures, came to light more as a by-product of the struggles of wresting political power within the profession from MD analysts post WW II when the government specifically invested huge resources into broadening the pool of providers to meet the growing needs of veterans (in the US). The pool drew extensively first from the large existing number of social workers, who used their orientation of social structures' impact on individuals as a basis for therapy modalities. That view morphed with the rise of behavioralist psych and the discovery of increasing numbers of psych drugs into the perspective of "fixing"--a rather mechanical viewpoint. Throw in a bunch of short-term interventionist modalities, and it's easy to see how clients could be seen as "broken" and in need of a pseudo-medicalized treatment.

The pervasiveness of those viewpoints also gave rise to a backlash of more humanist approaches. So today is a mixed bag of proliferating modalities, controversies at the heart of professional organizations, and most Ts describing themselves as "eclectic."