We pick the winner. The winner is not imposed on us by some apriori morality of the situation. It is clear to me that the most moral choice, if we care about that, is to support an alliance between the Shia and the Kurds, and that this is also the most expedient policy on straight Machiavellian principles ("the ruler of a new state must make all things new, subduing the proud and raising up the weak").
Are there Shia who are bastards? Sure. A lot of them with very strong prompting to it and excellent reasons to hate the Sunnis and all they have done, and are doing, both to themselves and to Iraq in general. Is that exploited by interested outsiders, including agents of Iran? Sure. So we have to outbid Iran for their allegiance, and we have to maneuver among the Shia we side with, to promote our clients and demote Iran's. That is how the game is played, absolutely elementary realpolitik 101. It is obscene that 4 years in we still have to talk about this and still haven't done it.
Should be have sidelined Sadr early? Of course. What is the strategy instead best designed to build him up? I'll tell you - letting the Sunni murder Shia with impunity and holding the Shia back telling them not to do anything about it. Then every frustrated Shia in Iraq who wants his community to defend himself, is driven in the arms of Sadr and Iran. That is what we have done. We have now taken it so far, we have driven the prime minister into the arms of Iran.
We should have let the Shia go after the Sunnis without restraint, as long as bombings originating in Sunni areas continue. We should have worked to exclude the Sunnis from the government, as long as (ditto). They should have been reduced to running for their lives to Jordan or Syria, or to turning in the diehards and the bombers themselves. No peace without a victory.
At the same time, we should have been encouraging the government forces to do this, not us, and not Sadr death squads. We should have marginalized Sadr by stealing his thunder, and framed him as an unneeded Iranian stooge. Tons of Iraqis told us this. Maliki told us this, Chalabi told us this. We decided this meant instead that they were too cosy with Iran.
We have played the whole thing as a tamp-it-down, get-em-all-to-get along pacification campaign, that tries to balance them all against each other. Balancing preserves all forces, but creating a government where they was none is not a matter of balancing, it is a matter of hegemony. A winner, someone who cannot be locally resisted without disaster. We are not such a force, we aren't permanent enough and everyone knows it. Neither is a government whose hands we have tied, because everyone knows it will not be permitted to hurt anybody seriously. Both the Sunnis and Sadr therefore have utter contempt for it.
It won't make a lasting peace, it won't stand up a dispassionate umpire government. There are rivers of blood and crime between them, and no one is going to forgive, or give up until they believe they have lost beyond all hope of recovery. We can destabilize the government as many times as we like before we go, Sadr or someone just like him will still be standing there offering a policy of outright victory to the Shia of Iraq, Iran will back that policy, the Kurds will be willing to settle for that outcome, and the Sunnis will get their balls handed to them on a plate.
We are just delaying Iran's victory. They already ran rings around us and kicked our tail.
Sunnis don't use car bombs on us (at least, not in Baghdad). Shi'ites use EFPs against us and have killed a hell of a lot of U.S. Soldiers with 'em. They're also directly associating with a nation very, very hostile to the U.S. that has also openly threatened the use of nuclear weapons.
So now tell me, who is the big bad guy sect now?