I agree with you, and I know hind sight is 20/20.... but taking Saddam and his military out (considering they were the only thing keeping some order there) was probably not such a good idea. I remember before we invaded Iraq reading an article that said 80% of everyone in Iraq hated the U.S. and would fight us to the death. That number is probably really close. That just means there were a lot more people over there to kill than we ever would have the stomach for. It means men, women, children. It means 80%.
It might well have been better in one sense to leave Saddam alone and spend effort on trying to funnel in a better successor when the time became ripe. The culture responds more constructively to monarchy than it does to attempts to be democratic. There are two rival sects of Islam and either one is willing (if not altogether comfortable) to be the underdog for a time, if there is a strong king.