I think, like others have said, that the issue is in the expectations around emailing and responses. You seem to expect and want much more than your T is willing to give.

For ME, I struggle with reaching out to others. I'm also much better at expressing myself with the written word. My T allows email because she knows it encourages me to reach out to her, and it feels like a "safe" alternative to me. Also, there are times when I need to be able to process a session and then express my feelings and that is easiest for me in writing. However, when I email my T, I know that she will only read/respond to emails once per day...usually in the mornings, and not on weekends. I know that she will not do therapy by email, and that her replies will generally be encouragement or affirmation of things I've stated in my email. If I ask her a direct question, and it's something she can easily and simply answer in an email, she will do so...otherwise, she'll tell me that we'll talk about it in session. I know that her replies will generally be brief, and I'm okay with that. I tend to limit my emails to no more than one or two per week, and simply don't feel comfortable with more than that...sometimes I don't email at all. My T has only one condition around email, and that's that if I feel I'm in crisis, I must call her (or a crisis line) rather than emailing. I readily agreed to that. We've talked recently about emailing, after I sent her a long, emotional email. After we talked about it in session, I apologized for "dumping" on her. She told me that she didn't feel I was dumping anything on her, because she knows that I will talk about the email in session. She would only have a problem with it if I sent the email and then refused to ever bring it up or talk about it or try to work through the issues I raised. When I email my T, all I really want from her is to know that I've been heard, and to put things out there that I might need help bringing up and talking about in session. So, her responses to my emails fit in exactly with what I expect and need.