I'd rather have as little to do with those Middle East barbarians as possible. While your idea is intriguing, it most definitely would lead to an all out war with the Islamic Muslims, which means every Arab state would join in too. Are we prepared for that? I don't think so.
I don't think so. Particularly if some of the oil income was diverted to the benefit of the Arab states that have no oil. Also, countries at a distance from the Gulf, such as Egypt, would have a great deal of trouble getting their armies into the fight.
All that has to be done is to seize the oil fields, all of which are very near the Gulf and under it, and a buffer zone. We wouldn't be interested in any other territory. The inhabitants could be suitable induced to leave the area involved.
Having most of the oil in the world under the control of people like the Saudis and Kuwaitis is a greater risk/price than the industrialized world should have to pay.