Saddam had planned the Insurgency before Baghdad fell. It started at the end of Ashura which coincided with Easter Sunday, 2004. I was in the Shia south and the Shia residents were warning us during a trip to Najaf that Friday.
My theory is that if our units had killed Saddam's army instead of bypassing so many of Iraq's army units to take the capital, the insurgency would have been one big fizzle instead of dragging out for years. A big war of attrition at the beginning would have killed the vast majority of the men who were willing to fight, thereby preventing the multi-year war of attrition that occurred right before we got fed up and left.