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I don't know if such an idea will work in a country where basic security and services such as water and electricity are at pre-industrial levels will work, but it is worth a try. I think you have accurately named what Iraq is: an unsolvable problem. There are no good options, just a lot of bad ones. And while I despise this administration, and a big supporter of progressive blogs/policies, I see too little of ideas such as this. I suspect this is largely because it is almost pointless to contemplate them, since even the chance of considering such notions at the political level is essentially zero.
We will not leave Iraq in the next two years, barring some remarkaable political changes in the US, and I doubt we will leave for 1-3 years following that, especially if a Republican is president again. We always assume we will leave, but look at all the troops stationed all over the world. South Korea, Germany, etc. It is not unreasonable to believe that the US will be in Iraq in some capacity for the next 10-50 years, given historical precedent.
Right now we have a Sunni centered foreign policy. Our main allies are Sunni dictatorial regimes (Saudia Arabia, Egypt). What if we switched to a Shia centered policy, with Iran as our chief ally? At least they have elections of a sort, and of course they have tons of oil.
One thing I do know is that as long as Bush is president, no new thought will be allowed.