Now I think we should just leave.

Ok. The Kurds would be pushed back north by the shiites and sunnis, until eventually hitting the Turkish border, whereupon the Turks, realising that they are the only NATO country with an immediate military interest in the area decide to annex Kurdistan. Bye-bye Kurds.
Next, the radical Shiites invite in some of their cleric buddies from Iran and get the Shia majority stirred up. Bye-bye Sunnis.
Unless, of course, the Sunnis invite in their buddies from Syria...Oh My God - it's going to be a Bloodbath.

Yeah, so what the USA _really_ needs to help patch up it's foreign relations is for civil war to prevail. The only credible justification left for the coaltion to be there to begin with is that they are preventing Saddam from carrying out further atrocities.

No one is sure of the total casualties during the Iran-Iraq war, but estimates range from 500,000 to 1 million dead, 1-2 million wounded, and more than 80,000 prisoners. There were approximately 2.5 million refugees, and whole cities were destroyed. The financial cost is estimated at a minimum of $200 billion.

Source

Those numbers would pale into insignificance. An oilfield with a power vacuum would result in a catastrophe.