Punctuality is important. My time on the other side of that appointment window is valuable time. I'd have no room to pick up my children in time, which could pose a huge problem for me as far as the schools and potentially child services.
So, no I wouldn't find regular tardiness acceptable, whatsoever. And wouldn't appreciate being billed for more minutes than what is being given.
I'd speak up, then start shopping around. Is there someone that your T is held accountable to? That's always an option.