I think the thing is, it's not a question of the US Soldiers dealing with Terrorism there, they could be there for another 100 years doing that, they might as well walk around carrying boards saying 'scapegoat', every little problem that arises, whether linked to the occupation or not will be the fault of 'them'. It's a gift horse from a political point of view.
Many confrontational leaders see themselves in a win-win position here, they can either do whatever they like or force a country that is already over-stretched and massively in debt to further push its human and financial resources, and create a swathe of world sympathy for themselves at the same time.
As Mefustae says, to pull out now would leave the country a raw turkey waiting to be plucked, and isn't going to happen anyway, because Corporate interests are about as willing to let go of those oil reserves as the average limpet is willing to let go of a rock. But I'll leave that alone before I start with my opinion on legal bribe... I mean Lobbying.
So, if they stay, they will be used as scapegoats for every tiny problem, but may achieve stability in the area, if they go, then there will be anarchy, and it will still be blamed on the US, and if they want to maintain stability in the area, I think it's going to take a talker, not a shooter, in my opinion.