Should the coalition pull out? That is hard to say. The coalition engaged in an illegal war of aggression. They hardly have a right to be there. I'd say they should be replaced by an international peacekeeping force from other nations entirely, but who the hell would want the job? It's very hard to restore order after you have whacked a hornet nest with a baseball bat. Someone is inevitably going to get stung.

If the will of the majority of Iraqis really had its way, there would be a Shiite Islamic governmnent installed in that country, and that would be bad news for Sunnis and Kurds, wouldn't it? Plus, the USA would not be happy about it.

This is what happens when an empire (the British) arbitrarily draws lines on a map and creates an unviable country and exploits the shit out of it, and then leaves, and a series of dictators take over to keep the lid on the boiling pot, and the USA backs one of them, and then decides not to back him, and then has a fight with him, and invades the place in order to exploit the shit out of it once again.

What does any of that have to do with democracy? Nothing. The present efforts at democracy in Iraq are window-dressing by the USA in order to justify what's really happening: imperial conquest of oil resources.