There are really only a small handful of historical cases where constitutions have actually exerted real authority over later generations, have actually organized or channeled social and political conflicts. Mostly modern constitutions are like bad peace accords between fundamentally antagonistic groups: a pause in a longer process of conflict. Even the US Constitution had that aspect to it, that it deferred a bloody and inevitable confrontation about slavery.
If the Iraqi Constitution cannot answer the question of why there should be an Iraq, it is because the elites writing it (and the occupying authority anxiously supervising the writing of it) cannot answer that question convicingly. The fault is not in the constitution itself, but the constitution is no solution, either.
Some blame the British-written constitution of Nigeria at independence for the Biafran civil war and persistent rumblings of secession or partition ever since. Not really, though the whistling past the graveyard in that original constitution didn’t help. It’s not even the classic old saw that Nigeria was a completely artificial entity made by colonialism, blah blah blah. Zambia’s a completely artificial entity. The Democratic Republic of Congo’s a completely artificial entity. The boundaries of Nigeria actually have some vague correspondence to actual historical connections between precolonial African societies, but the problem is that those connections were largely antagonistic or at least competitive between the societies of the forest and the societies of the savannah, woven together by the braids of the Niger River as it empties towards the sea. It’s not inconceivable that the remnants of Oyo and the territory encompassed by Sokoto could have reached towards some larger political amalgamation, but a constitution, no matter how written, could not do that in and of itself. It would have taken finding some pressing reason to make that union, something shared that was a positive product of local experience as opposed to a negative and reactive opposition to outside force.
If the Iraqis writing the constitution are just writing the prelude to partition, then the most helpful thing the US could do might be to midwife that partition now rather than deny its inevitability later. If the authors of the constitution can’t find a thing that makes them all Iraqi besides colonial inheritance and authoritarian repression by Saddam Hussein, then maybe there is no such thing to find. I can’t help but think that Nigeria might have been better off as three nations, or at least two. I’m sure that the Congo would have been better off as three or four nations.