Again, you don't have to take her up on it. But if you want to, I see no reason not to. Even if you're planning to see her forever, wouldn't you rather feel better as soon as possible?

And I know for myself, seeing my T a second time each week has really helped me feel more connected. I think I've said more in a few months than I had in the entire three years prior with her. I was always so anxious that I just couldn't get anywhere. But now that I see her twice/week, I finally am.

It seems like you're really focused on your T's feelings about you and about the relationship between you. That's good stuff to look at with her. I guess I'm wondering if you're seeing her offer as a sign of something else--her feelings toward you, perhaps--and if that's what's making her offer provoke strong feelings in what could otherwise be seen as a gesture that's focused on your improvement by someone who wants to see you be the best you you can be.