What Allawi was proposing, back 2007, was something very similar to the United States before we ratified the Constitution. Between 1776 and 1788, we operated under the Articles of Confederation, which allowed almost complete autonomy for our States. We even had 11 "Presidents" before George Washington. The reason you've never heard of them is they were elected by a relatively powerless Congress to one year terms, and other than financing the War, they didn't really do much.
Our Founding Fathers determined that the Articles were not sufficient for the new country's needs, so they drafted the Constitution, which brought more authority to Washington. Iraq has tried a top-down method from the very beginning, with most authority centralized in Baghdad, to the consternation of Kurdistan, especially, but Iraqiya is stronger in its own region, too, and would have benefitted from a decentralized system, at least until they became more comfortable operating within a more federal-type system.
It took us years, and we were a relatively homogenous society. Imagine if our Founding Fathers had been from competing sects with a thousand years of historical animosity. It still took them over ten years to become comfortable with a stronger central government. What Allawi proposed was similar to the way Switzerland, with its four languages, disparate populations, and many cantons, operates, and I don't think anybody would argue Switzerland, the Helvetian Confederation, is not a peaceful, functional society.