I'm going way out on a limb here, for full disclosure. In other words, I'm pretty sure I don't believe what I'm about to suggest. But could we be in Iraq, not for oil, not for democracy and human rights, not to profit the military-industrial complex, and not to benefit the GOP, but rather to promote an intra-Muslim war to achieve our security goals. In some ways, this suggestion reflects less poorly on the adminstration, since it at least ascribes a motive rooted in US security. Of course, it would be more pernicious in a way too, insofar as it would constitute religious warfare, potentially on the order of the crusades or Hitler's extermination of Jews.
However, its at least an interesting lens through which to view the conflict. Through this lens, the policy is not clearly a failure. The strategy fits. In other words, if a Sunni-Shia war was the goal, Iraq would be the place to start it. The Sunni-Shia divide appears, based on what I know, to be most pronounced and focal in Iraq, with other middle eastern countries more clearly in one camp or the other. Going to war in Iraq had the effect, then, of the Lex Luthor missile into the San Andreas fault. Clearly Iraq is fully embroiled in all out Shia-Sunni war now. Iran, a shia state, is already in the game, and is projecting new Shia power. Syria may also be in the game, providing training, equipment, and probably foreign fighters for Shia militias and death squads. Saudi Arabia, on the other hand, is funding the Sunni insurgents, and is likely exporting Sunni foreign fighters (also known as "Al Qaeda types") to the theater. Jordan and Egypt appear to be nervously on the sidelines.
Is what the adminstration wants to say, but can't, something more like "we want them to fight each other over there, so we don't have to fight them here?" It at least has the benefit of logic. It could possibly be true, whereas the platitude of "we're fighting them there so we don't have to fight them here" truly makes no logical sense, because nothing we're doing there pins "them" down or de-motivates "them" from coming here. However, if a Shia death squad killed your family, as a potential Sunni terrorist recruit, you might be more likely to fight them there, rather than heading to a camp to prepare for a terrorist attack against a western interest.
It should go without saying that I don't support this as a strategy, but simply wonder if it is an unsaid strategy. Part of what drives my theory is that it seems impossible that the adminstration is as incompetent as it seems to be. They can't possibly be capable of failing to reach their own goals so uniformly. I think they may be reaching some goals which they did not share with the rest of us.