Why not let the Iraqi people vote on America's military presence?

We have been in a heated debate for a while about whether or not to remain in Iraq, and for how long. If we truly wish for Iraq to be an independent state, why not allow them to decide? If we were to put pressure on the Iraqi government to put the issue to a vote, we would have a solid reason to either stay or leave, no question. In my opinion, it would be a big indicator to them that 1. we recognize them as a democracy and actually care what they have to say 2. we are not planning on staying there indefinitely, so they need to take their country in their own hands and start taking more steps toward stabilization 3. we aren't involved for our own selfish reasons (i.e. oil profits, imperialism, military posturing, a desire for a puppet country in a key region of the world) and truly wished to liberate them from an oppressive dictator and 4. we are there for them if they need us but respect their ability to make decisions, like a good friend and not an overly controlling parent.