I don't think that "mind game" is an accurate label for a therapist who has been consistent for months in saying that he will not answer emails and has welcomed her to send them and said he will read them. He changed his mind about what he is willing to do because of the impact it had on her therapy (and seems to have been right about that, from Lrad's conclusion). Changing your mind about the utility of what you do as a professional, thinking about whether it serves the person, is what I expect any professional to do. Which is his right to do as person, and his obligation as a professional (to do the right thing), because he thinks it wasn't helpful to her. I think he's only trying to do the right thing here, and that doesn't mean he has to be "consistent" like Lrad is a toddler or can't handle change.

Whether or not a professional answers emails and how that works cannot be judged by what you either must do because of your job and what you choose to do. Most people on a salary I expect have to answer emails as part of their jobs; in my work I charge people for emails and I also make strategie decisions about what is better for email and better for phone that depend on the person (I work with at least one person who for ESL reasons, doesn't do well with email or phone, and I usually just stop by her house to talk to her). I make house calls and I talk to people on the phone and I sometimes email or text or write letters, but it is important that I make good judgments about what kind of communication and when it makes sense to communicate. Something I'm also teaching my teenager. Saying anyone should always answer emails no matter what profession or the demands of how different people work is wrong, the way I see it. There are good reasons outside of the profession of therapy to limit or be strategic about communication types, including email. No client is entitled to have email answered, especially when a T works on an hourly rate.