However, I really think if we were going to invade, then yes we should have taken the country and made is US territory.
I disagree. When it works democracy does so because it gives people with different voices a say in the system, alleviating the need to solve differences with violence. You may contend that the Iraqi people are not currently suited to democracy, but for the US to autocratically rule Iraq it would be forced to do so with an even more brutal hand than Saddam Hussein, since you've not only ruled out democracy but must rule as complete outsiders devoid of ethnic glue. Doing so would be for the US to lose a piece of its soul.