The problem with partition is that it left the Sunni Arab region landlocked with no natural resources, an oil rich Shia region with even stronger ties to Iran and an independent Kurdistan which would drive Turkey nuts. The worst part was that having a bitter(at being deposed by us), dirt poor and loosely governed Sunni Arab state on the Syrian and Jordanian borders wasn’t an ideal outcome for our purposes. We were afraid they might become infiltrated dominated by Islamist elements that would leak back over into Jordan and Syria.
Of course the current situation is far worse, so hindsight is making partition look like the best bet.
Hmm, so it sounds like the problem was the people. Many people on FR said the solution was a “no state” solution: turning Iraq into a parking lot.