That's fine, assuming that Sunni and Shia will settle into a resumption of the stalemate that has existed for centuries. But what if each side of that ancient conflict sees an opening from the Iraq War to gain an upper hand over the other? I think that the major reason that Bush, Sr. did not go into Baghdad back in 1991, was that it would lead to a resurgence of Shiite influence, and he was wise enough to see that Jimmy Carter had already done enough damage in that direction by making conditions ripe for the ayatollahs to resume rule in Iran.
Simply put, we could manage Islamunism until that point. Arab states would come together in hasty coalitions, fight Israel, get their butts kicked, and go back to sulking in the desert for a decade or so. The only retaliatory weapon they had against the West was to raise the price of oil, and we'd move to deal with that by conservation measures, and increased domestic production.
We shifted to a different management scheme under the Reagan Administration, we kept the Iranians and the Iraqis busy with each other, trading weapons for hostages to the Iranians, and giving military information from our satellites to the Iraqis. A million Islamunists killed without US troops being at risk was the payoff there.
What's wrong with returning to that strategy? We have the Shiites in Iraq feeling more power than ever, and a crackpot Iranian leader willing to pour his country's blood and treasure into helping them, we have nervous old-line Sunni states with more money than Allah being willing to fund their brothers, the former Baathists, and they're all ready to start killing each other off. We have Kurds with their first-ever homeland, and the Turks (certainly not our friends after 9/11) wanting to go to war with them, proving that they're not ready for prime time as Europeans.
Why are we standing in their way?
Energy. And our access to it, in one of the most unstable regions in the world. And countering the influence in the region of traditional adversaries such as Russia.
And nuclear arms proliferation.
What a pea soup.