There are 2 reasons why I don't compost t bags. First in my experience the bags don't rot that well so when using the compost you keep having to fish out wee scraps. The second is that tea is full of tannins which are I understand are designed to stop decomposing bacteria (think of tanning leather). Fortunately our council collects kitchen waste weekly so that has slightly solved the issue for me.
Incidentally I recently bought loose tea by mistake so have gone back to making a full teapot, tea cosy, strainer, the lot. It tastes so much better than a one cup, or even tea bags in a pot that I might not go back to tea bags.