I'm not sure if this is a helpful comment, so if it is not please ignore it: Inwonder whether this sense that therapists are blaming you comes from your feelings combined with the nature of therapy.
What I mean by that is that the job of a therapist - I think they would all see it this way - is to help people to overcome difficulties and have better or happier lives, in one way or another.
So if someone comes to them and says that they are unhappy because of XYZ (e.g. Feeling or being socially isolated), then the therapist needs to first look into why this is the case,or what could be the underlying problems leading to the person being in this situation, in order to formulate what kind of therapy would help and what the goals would be.
If you are feeling that your problems are flaws, then I wonder whether a therapist trying to share with you their understanding of the underlying problems that could be addressed in therapy, would feel or sound to you like a therapist listing off your flaws?
For what it's worth, I don't think problems are (necessarily) flaws, and I think they are part of being human, and I guess some of us have more problems than others and I think that is partly just due to our luck. Not because we are flawed.
When I first went to therapy, I assumed that all of my problems were flaws. I had always seen myself that way. Through therapy. I gradually learned to see things differently. When my T first shared that he didn't think I was a bad person, it sounds silly now but that really floored me, and it took me a long time to really understand.