I used to feel that the T's personality really didn't matter, it was more important that I have someone to talk to, regardless of who that person was. But still I think it matters that T is a person different from me, who can ask questions I wouldn't think of and spot patterns of behavior and thought that I wouldn't be able to see. For example if I talk about a situation where I felt an older woman was criticizing me, my T can point out that my mother criticized me a lot, that I often feel criticized by older women, that this is a pattern and maybe I need to question whether my feeling is grounded in this instance or if it comes from somewhere else, or why it bothers me so much.
I think we all have basic assumptions about how the world works and how relationships work, and basic ways of thinking about things, that it's very difficult to perceive in ourselves. If there's nobody to challenge those fundamental things or at least bring them to consciousness then they won't change. So an imaginary T wouldn't cut it, I don't think.