Let's Settle the Civil War in Iraq

There's a lot that's wrong with the Iraq war, but I still don't feel as if we've quite gotten to the bottom of it. Put aside for a second the phony weapons of mass destruction, the civilian casualties, everything that on the surface makes this war so wrong. Now focus only on the political element as it has developed since the war began: the minority Sunnis battling U.S. backed Shiites and Kurds. Recall that at the start of the war, coalition forces were fighting against the Iraqi army, Saddam's Elite Guard, and other assorted rag-tag militias. The Iraqi army ran away and then was disbanded after the fall of Baghdad, the Elite Guard never did much damage, and after initially getting bogged down by the militias, the U.S. forces moved on to Baghdad and left the British to mop up. Yet, after the fall of Baghdad, coalition forces continued to face an enemy and still do. The logical assumption then, is that it is the same enemy - the one we came to fight, and therefore, an enemy we must continue to fight until it is defeated. Yet, is this really true? It may be true in one sense that many of Saddam's loyalists were Sunnis and they comprise the core of the insurgency. The reasons that they are fighting, however, have changed completely. They are now fighting not to resist a foreign invasion but to oust the foreign backers of the ruling government, to reclaim control of territory that once belonged to them. Notice how the cards have changed. Setting a great deal aside, one could plausibly claim that the coalition forces fought the Iraqi army because Saddam was bad and deserved to be ousted, but why should we now be fighting the Sunni insurgency because it wishes to reclaim territory from its Shiite rivals? In other words, the U.S. never set out to intervene in a local dispute between Sunnis and Shiites, nor can I even imagine any politician suggesting that we do so. But that is what the Iraq war has become. Strangely, no one questions this. Democrats such as Hilary Clinton and John Kerry have stated repeatedly that the primary "exit strategy" for the U.S. must be the successful training of a new Iraqi army - i.e., a Shiite army capable of repelling the Sunni insurgency. This is the new mission of the coalition. Everything is predicated on the success of equipping and training this force. But why should we? One might argue that the tactics of the insurgents are evil and this is certainly true, but from the perspective of U.S. interests the dispute between the parties is purely political, and their current alignment is aribitrary. The Shiites have welcomed the American backed political process, knowing it would benefit them, the Sunnis have rejected it for the same reason. There is no difference between this rather mundane local affair and any number of conflicts around the world, most of which the U.S. takes no side in. Rather than waste our time and resources equipping one side against the other, the results of which will surely be a bloodbath, we ought to be trying to settle the conflict. If we could convince the Sunnis that a reasonable political settlement awaits them, the culmination of which would be the withdrawal of coalition forces, why wouldn't they agree to it?