It is now conventional wisdom that the USA should have ignored the Iraqi parliament and stayed in Iraq with a large military presence. This forgets that is was our presence in Saudi Arabia that first put the USA on Osama's hit list. The statement shows that a sovereign Iraq is not something we will tolerate. Now if we merely colonize Iraq it will cause a backlash that will make ISIL ( daesh) grow in numbers. Thousands and perhaps millions of Iraqis have died since 2003 due to the wars. We need to offer them something that would make our permanent presence in Iraq palatable in exchange for their deaths. We need to offer Iraq statehood. This may sound insane but it might make more sense than the alternatives.
A large problem with our presence in the Middle East is that we are seen as the inheritors of the British empire. The British, like the Romans, would use a local indigenous ruler ( under British control) to more efficiently run the colonized province. Apparently the people we pick to be our local leaders are not well vetted. See Chalabi. Maliki etc. Statehood would be something Iraqis could believe in because it is obvious that Daesh fighters are more motivated than Iraqi soldiers. This would also crush the idea that the USA is anti-Muslim and it would re-establish the idea that the USA is not a 'blood and soil' nation but the new nation based on an idea we always claimed it was. Of course they would first become a territory but this is a more aspirational than being a colony. Statehood for Iraq