So no ethnic states at all - just areas that people lived in - and you left out the huge mixed area in the middle of the region as well the mixed usually secular nature of the dominant political organisations for much of the history of modern Iraq, the mixed nature of the tribes. Don't paint myths as history.
on this topic i read this yesterday:
"The sectarian myth of Iraq
We coexisted peacefully for centuries, and need neither brutal dictators nor western intervention"
http://www.theguardian.com/commentisfree/2014/jun/16/sectarian-myth-of-iraq
Until the 1970s nearly all Iraq's political organisations were secular, attracting people from all religions and none. The dividing lines were sharply political, mostly based on social class and political orientation. The growth of religious parties followed Saddam's ruthless elimination of all political entities other than the Ba'ath party. Places of worship became centres of political agitation and organisation.
Despite popular myths, the majority of Ba'ath party founders were Shia. However, Iraqi Ba'athist ideology always had a racist dimension against the Kurdish people and non-Arabs – as well as a class orientation, when in power, that marginalised millions in the poorest sections of society, mostly in the south. Southern Iraq and some areas of Baghdad, populated by mostly Shia migrants from southern rural areas, have historically been home to the poorest people.
Iraq's biggest mass organisation from the 1940s to the 60s was the Iraqi Communist party, founded in 1934 by activists from all religious and ethnic backgrounds. It was the strongest party even in Iraqi Kurdistan, and remained a mass party until its leadership decided to join Saddam's regime in 1973 – against the wishes of most party members. Saddam launched a vicious campaign against the ICP in 1978-9, and the party lost its raison d'être after joining the Iraq Governing Council set up after the occupation in 2003.
Commentators on Iraq often refer to ethnic wars waged against its Kurdish people. They fail to mention that none of these wars were popular but were ruthlessly pursued by repressive regimes, particularly Saddam's.
etc
I imagine the reality is a grey area