But there is no inherent reason why the "terminal" at which you check-in needs to be the same as the one from which your flight departs.

Whoever came up with the idea of naming the check-in areas T1 and T2 obviously has no real-world experience of multi-terminal airports. It would be far more sensible to call the check-in areas something else entirely (name them after colours and do the signage accordingly perhaps) and use the word "Terminal" in the sense that it is used everywhere else in the world - i.e. the building from which the passengers board the aircraft.