My t is private practice. To my knowledge, she is the only one to read her work emails. Aside of the general lack of confidentiality of using electronic communication, I don't think there are many confidentiality concerns. Even if someone hacked her email and read what I sent (or hacked my own and read it), I doubt they would get anything useful.
T seems to only bill for face to face sessions. I guess if we had a phone or Skype session, she would bill for that, but since we really only do f2f, she doesn't bill for anything else (nor does it take that much red tape to get an email response from her).
I would be frustrated by that level of complexity around contacting t, especially with an email about scheduling!