That sounds really clumsy, unskilful and even somewhat cruel. A therapist might not be your friend, but the relationship is designed to be deeper and more transformational than most friendships are.

I personally wouldn't and don't have time for therapists who think they can sit in a safe little tower keeping themselves completely separate from the client. There's no relationship when one party isn't engaged or known in any way.

Definitely worth discussing further with your therapist. There's nothing wrong with not feeling safe sharing with someone you don't know at all. Most of us don't.