To add a little more color to the picture, the free but struggling Iraqi democracy will probably be forced to curtail individual liberties to fight the continuing insurgency, and the democratic majority of the population might well be in favor of closer ties to the hardline conservative theocratic pseudo-democracy in Iran.
If the US sees this happening, odds are it will not want to pull troops out and give up control in such a strategically important oil rich country. The presence of US troops will continue to foment the insurrection.
Or maybe the whole country will have a meltdown into 3-way civil war right in front of us anyway, with our troops caught in the middle. That's what Bush Sr was concerned would happen and one of the reasons he chose NOT to go into Baghdad and depose Saddam in the first Gulf War.
Unless we start pumping and selling their oil ourselves, I don't think it will have been worth it economically.