The ones I see are in private practice as solo practitioners. They have no staff.
The first uses email - it is published on her website and she invites the use of it.
The second does not have an email address published but has a cell phone number that she gives to clients and encourages use.
I see no problem (other than insurance = which I do not use) for the therapist to charge for emails in 10ths of an hour just like I do when billing as an attorney. The one I see has never made mention of it -but I don't see that it would be unfair to bill for it. The second one stated up front that she bills in 10ths of an hour for phone calls over 15 minutes - again - fair enough as far as I can see. The second one does not take insurance at all.