I am one of those folks who gets to email my therapist as often and as at length as I want and she nearly always replies in detail. However, I pay for the service, otherwise I would, too, consider it working for free and not be comfortable with so much email at all.

You know.... if you feel what is best for you is to be able to do therapy via email as well as in person, there are therapists you can find to do that with, if it's really important to you.

Email hasn't been perfect for me: I had more misunderstandings with it than I do now, for example, but overall, I've found it invaluable and would not see a therapist who didn't allow it. I am happy to pay for my therapist's time writing to me and appreciate having written records for reference.