Turkey, however, is positioned almost ideally having common borders with Syria and Iran (Or is it Iraq? Or both?) on one side, and with Greece, Armenia, and Russia on the other. Thus it also wins on location, location, location.
If the assumption is that NATO is who wants to go to a fight in the Middle East. I am not convinced.
But no worries, two people can look at the same geostrategic situation and arrive at different conclusions. If one presumes that NATO is, in a unified sense, committed to going off to fight in the Middle East - Iran, Syria, Iraq, Israel, Lebanon, and so on, yeah, what you laid out makes sense and fits a perfectly TurkoCentric view of the Eastern Med.
Eastern Med.
The NATO Southern Region goes from the straits of Gibraltar to Istanbul. Not just the Eastern Med.
I do not believe that NATO is so committed. (The US might, or might not be, depending upon which clown-of-the-week we have in the White House)
Aside:
I worked for a Turk for about 3 years in NATO. Good man, and I hope Erdogan's purges have not harmed him. Learned quite a bit from him about trying to see the world from a Turko Centric view. Enlightening, to say the least.