I see things from both sides.
Maybe he is trying to set up good boundaries, but also, you need someone who is there for more than 45 minutes a week. Put it all together, and you get a bad fit!
There's nothing wrong with that. I don't think that ANYONE should go into trauma therapy if they aren't willing to take a call in between sessions. It's pretty much saying "I'm yours for only 45 minutes a week, if anything else arises, you have to figure it out on your own because I'm not helping" Now is this really helping someone who is working through trauma? I have my doubts.
I can see him not wanting to answer 45 emails (or even read 45 emails), but there needs to be a happy medium. IMHO he is being VERY heavy handed by saying "no contact between sessions" I think you should look elsewhere for a therapist who is at least willing to pick up the phone if you're having trouble between sessions.