Iraq wasn’t all that stable even under Saddam. Why else did he need to gas the Kurds, flood the Marsh Arabs, etc.?
Iraq’s instability was a function of its artificial borders. The country was rested out of the remnants of the Ottoman Empire after World War I, and it was cobbled together with different sects and cultures that never would have been part of a unified country if left on their own.
Establishing “democracy” in a place like that is a recipe for disaster.