Iraq is a deeply polarized society, with Sunnis, Shias, Kurds and other minorities deeply distrustful of each other. Despite this, Saddam Hussain was able to unite them, although by applying force. He suppressed the radical Islamists as well, making the lives of minorities (Christians, Yazidis, Mandeans.etc) easier. Once the Americans overthrew him, the Islamist radicals immediately rose to power and caused problem for the minorities. 80% of the minority population has vanished from Iraq during the last decade.
Iraq needed a federal republic after the occupation. Each region with real representation in the legislature would go a long way toward their various groups feeling enfranchised. Of course not breaking it in the first place would have been good as well.