President Bush should have resolved this dichotomy before the invasion. My preference would have been to tell the State Department that their objections are understood but we're not "nation building".
Perhaps if the Administration understood just how awfully thirty years of Saddam had destroyed the fabric of Iraqi society, they wouldn't have tried to unleash "instant democracy".
It's like that old saying that where social standards exist, laws are not needed. Where they don't exist, laws are ineffective. When people have been forced to lie, cheat and steal for decades just to stay alive, law and order cannot quickly return. Just as Pakistan and Iran have gone from modern societies to places where villagers gleefully stone women to death for being raped. That can't get flipped back overnight. You would need an entire generation to live in a society where good was rewarded and evil punished for decades before good became the norm and crime the exception. The post WWII occupations of Japan and Germany would look like cake walks in comparison.
There is a middle ground between "nation building" and "no ground troops": The ground troops accomplish the military objective and then GTFO. The only way that could have worked in Iraq would be to put an Iraqi strong man in place right away.
From a larger perspective, perhaps having British cartographers define country boundaries wasn't the way to go.
The book The Generals, by Thomas Ricks, is a history of civil-military relations in the US. It has a chapter on the utter failure of both the President and the generals in command in Iraq to agree (or even recognize the need for an agreement) on what the desired "end state" should be, and what actions had to be taken to reach it. This wasn't the only problem, of course, but it was the root problem from which all the others flowed.
Another good book on the Iraq disaster is We Meant Well, by Peter Van Buren. The author was a Foreign Service Officer involved in "reconstruction" in Iraq. His tale of how the "occupation" was botched, despite the best of intentions, is enough to make one cry.
That partition has kept tribal/religious factions within national boundaries at each others' throats for some time--which may well have been the intent.