Nice suggestion there but not feasible. If we were to divide Iraq into three parts, that will admit our occupation was a failure and we would be forced to withdraw troops quickly. Once that happens, Turkey will invade Kurdistan and enlarge the "Turkish Empire".
I would set up shop in Kurdistan. Big Airbases, lots of concrete, parked tanks, free innoculation shots, American troup patrolling a DMZ between Turkey & Kurdistan, the whole 9 yards. If our Turkish "ally" invades our new Kurdish ally when we're busy helping them create another autonomous zone in Iran, well, they have to cross that there DMZ & kill Americans to do it.