The problem in Iraq is not that there aren't organizations capable of administering society, it is that there are several of them. You have a well armed population (not in comparison to the US, but enough for a sustained civil war), a Shia majority that wants one form of rule, a Sunni population that is used to leaders from its ranks being in power, and a Kurdish population in an oil rich region who would like their own territory, which neither the Sunni nor the Shia would be interested in letting go of (or for that matter the Turks). And this is just the major power groupings, saying nothing of how each of them break down into competing tribes and factions, secular and religious interests. And this also doesn't include the regional power interests who would like their say in how Iraq's will look religiously, ethnically, politically and militarily.
Added to this are the pent up pressures from thirty years of Saddam's rule being suddenly released.
If there was a lack of power concentrations or power was totally diffused throughout the society, that would be a better scenario, but when there are a multitude of power bases with possibly competing interests, that makes things much more volitile and complicated.
I am definitely not saying that I think that the US Army occupation will uncomplicate this situation (I think, perhaps, it increases the problems), but I do believe that any realistic solution must really take these factors into account.