My former T charged for reading and responding to emails and for the time that he spent "considering my email and his response." It was usually the equivalent of 15 minutes of his hourly rate. He did not allow email messages.

Current T welcomes email and text messages but I have never sent them. I never wanted to started texting or sending emails and then having T erect a boundary and stop allowing them.

I think that it is fair for a T to charge for their time which includes emails, text messages and lengthy phone calls.