The Kurdish state would have the prospects of being a very good ally to the USA, though at the heavy cost of other strategical partnerships.
How so ???? One of the main Kurdish parties is an Iranian backed "terrorist" organisation
Until the recent ceasefire agreement between the two main parties they spent as much time killing each other as they did fighting for "independance" .
Plus you have the various other Kurdish grouping both within the Iraqi borders and outside of them , fighting amongst themselves and neighbouring governments , what the hell makes anyone believe that an "independant" Kurdistan would be either peaceful or a "good ally"

So to examine 3 seperate states in Iraq ;
Kurdistan , bordering Turkey , Syria , Iran (each with significant Kurdish populations and the problems that may entail) and ArabSunnistan (may be a bit of bad feeling there for some strange reason) .
ArabSunnistan , bordering Kurdistan(already mentioned) , Syria(Ba'athist , so they may be friends) , Jordan , Saudi(home to exremist militants) Iran (that should be fun) and new Greater Iran (Shiastan) a few more problems there don't you think .
Greater Iran , bordering Iran(oh no the axis of evil) Kuwait (don't they still claim that that is really their land and oil anyway), Saudi and ArabSunnistan(here we go again)

So instead of a nice pleasant little civil war in one country you have the very real prospect of a regionwide conflict involving 9 countries with ever shifting alliances . Just think of Lebanon....but bigger .. and with lots of impact on oil flow .

So in my opinion splittiing the country would cause a lot more harm than good , but of course anyone with half a brain would have thought about the aftermath before they invaded .