And that is the million dollar question Cap'n!
I think the truth will out in time. The military accomplished its mission but then State got involved and mission creep became the order of the day and the following decade. We should have followed the old pattern and broken Iraq up into Kurdistan, with separate stans for the sunnis and shiites. A partition along the lines of India, Pakistan and East Pakistan. They would have happily warred with each other to the end of time and been no threat to anybody but Iran.
So true. And, like Perfidious Albion, we could have played them off against one another with guns & bribes until the end of time...no attempt being made to actively "run" anything, but rather controlling those who DO.