Compared to the inventory and personnel size of the TAF, the power multiplier used in these operations are mostly minimal. Many of operations are not even appreciable as used invetory and troop sizes.
Since decades, The National Security Policy Document of the NSC has been planned according to the thesis that if Turkey enters a war, it must fight 3 states( and half is asymetric /proxy threats) at the same time. We never want to experience such an event with Greece here, but against this risk, the only interlocutor of the Greek army is the 4th Army, which is independent structure from NATO. Not whole TAF.