My T responds to every email I send. I don't email her that often. But she will let me know that she got my email and she responds on what I wrote and that we'll discuss it in therapy. I wouldn't like it if I didn't get a reaction.
For my T it's part of her work. She gets paid for a certain amount of hours. Those hours she is in her office. When she doesn't has a session, she does paperwork or answering emails.