From my point of view, it's your dependency on the replies that is the issue. What if she's sick? Dealing with an emergency? And you expect her to reply always? And if not, you're at risk for a crisis?

My T lets me email her as much as I want to. I can ask for a reply in the email, but that doesn't mean she will reply. And her replies tend to be the same: got your email, lets talk about it next session, everything is okay, have a great weekend. Sometimes she replies the same day. Sometimes it's several days. But her lack of response doesn't effect my situation.