Is Division so Bad
The borders for most countries in the Middle East and East thereof were drawn rather arbitrarily by the British, many times not taking into account the terrain or the indiginous population. Iraq is one such structure. The British got hold of this land after the Ottomans were defeated in The Great War. They drew some lines on a map and appointed a Hashmite Royal over three very different peoples. This is a further justification for creating three autonomous regions in Iraq (see http://voiceandview.blogspot.com/2006/09/way-forward-on-march-24-2006-i-wrote.html) if the on going civil war is not considered an adequate one.
The problem, for the US, is that this strategy makes Iran's presence stronger in the shi'ite region. It also makes Turkey, a staunch NATO member during the cold war still an outcast from the EU after many of the Soviet sattelites are a part of it, now more worried about its eastern flank. However, It is probably best for the people who live in Iraq but are increasingly not Iraqis anymore.