I think a good T would be fairly interchangeable, but it does matter in at least some aspects. Even with a blank slate T, they aren't just a mirror. The way I like to think of it is-the T takes my projection, transforms it into something with meaning (and hopefully attached with something good), then I introject it back in from the T. The introjections serve as building blocks of the self.

In becoming who we are, we spent years introjecting our parents projections, sometimes toxic. The point of a blank slate T, in part, is to leave their stuff out of what is projected back into us. That's how you can really figure out who you are.

A T has to be good at that-taking in our projections and leaving their stuff out of it. I would never see a T with a mental illness for this kind of therapy.