Excellent question.
Persia (Iran) has existed for 3000 years, more or less where t is today.
"Iraq" was invented by the British Foreign Office in 1922, has no native people and no natural boundaries. They merged three Turkish provinces: Mosul (Kurds), Mesopotamia (Sunni Arabs, Chaldean Christians, Jews) and Basra (Marsh Arabs, Shiites).
Why they did this, I don't know. Why we decided that a guarantee ot the territorial integrity of "Iraq" was a good idea, I cannot fathom except as some kind of misguided multiculturalism.
Do you think it is misguided multiculturalism, or is it resigned pragmatism? When you start thinking about the ramifications of breaking the "country" up (such as it is), it boggles the imagination. The south would undoubtedly align with Iran. This would leave the center landlocked, and would essentially make Iran a "bordering neighbor" to Kuwait. It would seemingly make Iran a huge oil producer.
It would lead to the creation of a Kurdistan to the north and possibly destabilze Turkey. We might gain some short sighted gratification fom seeing Turkey suffer, but they are the only democratic Muslim state, and a NATO ally.
It probably is best to leave Iraq intact and see if it can function as some sort of federation. It ain't gonna be easy.