I have been there too :/ (still there actually, I'm just trying to look at it differently).
I bet your T wasn't wishing the hour would fly away because otherwise he wouldn't have chosen to be a therapist. I was feeling horrible because of that too and hadn't addressed it until I realized it was painful. So I talked about it and my therapist actually thanked me for telling her how painful therapy was becoming for me adding more anxiety to my existing issues - because I looked so independent and distant and she thought I was in no way attached. Eventually I came to the conclusion that yes, it is a business relationship, but her care is "for free" and it is always there because she is human too. And that I need her as a therapist now, I needed a T in the first place and I was lucky enough to have such a good T to wish she could stay in my life. It's painful, but my previous T was horrible and if it's true I didn't have this attachment problem - well it lasted very short at least - it is also true that she damaged me more and I still see the effects.
What did your T say about the session? Your feelings are 100% valid and understandable. We get the care we never had and this is part of the healing process I think...