I don't know about actual failing, but I understand what you are trying to say. Basically, I think, you are asking if therapists honestly admit when they didn't do a good job with the client. In most cases, the answer is, unfortunately, no. There is a lack of honesty in the profession, but there is a lack of honesty in many societal institutions and structures, so therapists, by no means, are the only ones who often don't take responsibility for their screw ups. This has nothing to do with being coldhearted but rather with the fear of hurting their egos by admitting the mistakes.

It is also and mostly a structural or systemic problem. Many psychotherapy methods are based on myths instead of scientific research, and those myths have been perpetuated for decades and have turned into a dogma. This is another vulnerable spot of the profession that many therapists don't want to address and get very defensive about it. So, yes, I see your point and the point is valid.