Surely you didn't think you could leave an IraQ that wouldn't be influenced by Iran. The population of Iraq are majority shiite, certain things are obvious in a hostile world and one is where you form alliances. The conflict in Syria is shiite v sunni, the conflict in Iraq is now shiite v sunni, I predict Iraq will break up into states for each of its peoples, and the map of the middle east may be changed with a break up of Syria too. this is the only way to settle the conflict.
It doesn't suit the US to start a fight with Iran, they want to unravel from Afghanistan not be embroiled in a middle east war