re: You're good at research.
Are you aware that (according to the Geneva Convention) as the occupying power, the U.S. has the primary responsibilty for the safety and security of the people of Iraq? The Iraqis may blame the die-hards for killing other Iraqis, but they'll also hate us for not stopping it.
And the Powell doctrine would probably be followed in Iraq if it wasn't for the fact that widespread indiscriminate killing (like we did in Vietnam) would be counter-productive.