While it's true that Sadam's military was full of essentially modern day Nazis, [...]
Saddam was not a nazi. He held a iron grip over muslim factions that can't help but to kill each other. And that is exactly what they did once Saddam was removed.
Saddam Hussein was not a model leader but he was a 'moderate' if such a thing can exist in the islamic word. He also was the only one able to control all these retarded Muslim and keep them from murdering each other. He also was the only one capable of protecting the iraqis minority of other religious faith.
All the claim that he killed babies or gas villages are lies. Not believe the CIA in the 1990s made you a tinfoil-hat'er, still believing them in 2014 make you a fool.
The truth is a bit more complex. The Sunnis weren't all that upset about getting rid of Saddam. What really ticked them off was when L. Paul Bremer disbanded the Iraqi army (sending a couple hundred thousand Sunnis out into the world with no job, no money and guns) and then fired every Sunni in the Iraqi civil service.
Only then did we start to see lots of internecine violence.
Then we brought in Nuri Al-Maliki who systematically discriminated against the Sunnis in all walks of life. Which just made things much, much worse.
It was about economic and political power. Once the U.S.bought off (with huge sums of money) the Shia and the Sunnis, the violence largely stopped. After the flow of money stopped when the U.S. left Iraq, the systematic discrimination by Al-Maliki's government pushed the Sunnis right into the arms of what would become ISIS.
Even that is an oversimplification, but there were failures on all sides, and everyone is a loser.