The problem's much greater than who owns it. After failing to disintegrate ISIS as soon as they marched across the desert, they're unstoppable. Then, besides that, his administration (with the blessing of the 'pub war-mongers) STILL worked to arm, fund and train Syrian militants who turn and join ISIS. At that time, the only thing that would've made sense is to support Assad.
Now, ISIS is going to own a huge chunk of Iraq and a corridor to the Med through Syria. Take out the map....it won't be pretty. How does Western Civilization survive that?
Just wait till they start moving into Saudi Arabia. Even more barren than Iraq, which means huge territory can be captured by conquering a couple of villages. Plus, they’re already struggling against the Houthis