I understand that thinking, and as far as might be done on a "what if" basis, I disagree with the premise that it would have been a war-shortening thing to have bought the Iraqi Army, instead of disbanding it. Why? (1) Because more things were considered through the high diopter lens of near-chaos and insurrection. By the Iraqis, by us and our allies. Those lessons of what happens without an effective police and government among a population at violent odds among itself are worth the tragedies, sufferings and pain, long term. (2) That bought Army would have itself been unstable and caused great trouble in ways we can only now imagine.
What we have now with them is not perfect by far, but I suspect that relationships man to man at every level are stronger for having been tested and proven. That's a foundation for building.
A bought army is no foundation for anything but trouble.
Keeping the army would have had issues, and would have required strong debaathification, but they would have paled compared with 3+ years of sunni insurgent activity is my point. Hindsight is 20/20, but ... History will have to judge.