You're right...I believe we're in the northeast region near the Turkish, Iraq borders and Kurdish areas...so our presence has the immediate effect of protecting Kurdish allies, more than Israel.
But, our presence - wherever it is - implies, if worse came to worse our nuclear weapon capability. That was our initial position in Western Europe. When our NATO allies doubted our commitment, we upped our troop levels to reassure them we would use our nuclear umbrella in time of a ground attack.
A nuclear deterrent negates the ability of either party to use their weapons against their enemy...due to the fear of retaliation. Israeli's nuclear force is a deterrent only as long as it can be used free of that fear. IF Iran develops its own nuclear weapons it negates the Israeli nukes. The absence of an Israeli nuclear deterrent, increases the probability of a non-nuclear, conventional ground war...and that's where a significant U.S. presence in the region acts as a deterrent.

Link: http://www.vin3.org/index.php?c=article&cod=34158&lang=EN#vin3Comment-145406

Bolton, accidently or not, did the right thing and Trump double-crossed him. The Turk told Trump to pull out and Trump, have not having even a gradeschool concept of diplomacy, agreed in a tweet with no conditions on the Turks, without whom we can't build or maintain the f-35, and who then openly said they will liquidate all Kurds in Syria. Erdogan then Threatened the US, and Trump with retaliation if he objects, and Trump is silent. One of the reasons for the wall follies is Trump trying to cover his cowardice and ignorant mistake. Pull out of Syria and US influence in the Mideast goes to zero. Nice, Trump. Real nice. Real fluking nice.

Link: http://www.vin3.org/index.php?c=article&cod=34158&lang=EN#vin3Comment-145405