After 4 years my T decided email would be ok. I had asked about it a couple of times and she declined, so when she told me out of the blue that I could email, I was surprised and asked why she changed her mind. She said that when she first considered it, it sounded like it might be too cumbersome and would require more time than she had available.

We don't email back and forth, though.
I email and generally she emails back just to say that we can talk about it in session, pretty similar to how she handles phone calls. She has always offered phone contact including her cell. The last email response I received from her was:
I can see how hard it is to say these things and you do write so clearly. I hope we can talk about these thoughts and feelings in the next session.
So that's how it goes for us.