Great post, but very respectfully I think you're missing the main point, which is that THERE IS NO SUCH THING AS AN IRAQI.
There are Sunni Arabs, and Shia Arabs, and Muslim Kurds of various flavors, plus a few Chalean Christians, Turkomen Shias and so on and so forth.
But there are no Iraqis.
The great mistake of Bush II's foreign policy is that he naively thought that just because an area on the map says "Iraq" or, say "Rwanda" that the people living there are correspondingly "Iraqis" or "Rwandans." Turns out that simply isn't true.
The Hutus and Tutsis living in the contrived, designed-to-fail political entity called Rwanda sure didn't see it that way.
Nor did the various tribal and religious communities uneasily sharing a Brit-created entity called "Iraq." Whatever our policy should be, to be sane it must begin with the facts as they actually are, and the most salient of those facts is that there is not, never was and never will be any such critter as an "Iraqi."
The groups you are referring too, “Iraqis”, since the beginning of the Muslim era, in the south central core of “Mesopotamea” had been administered/governed most of the time through one governing administration all the way into the Ottoman era, with the heart of the administration either in Baghdad or Damascus, regardless of the diverse groups in the area. What they did have very often within that administration was a lot of local autonomy, as long as the central administration dictates were obeyed. No, it was not in our way of thinking a “nation state” in the modern sense, but governed together yes the diverse people of the area were.
One of the key historical problems in the area has always been the Shia-Sunni split, and the vast majority of the time Sunni leaders have had the central governing authority whether or not Sunni Muslims were the majority or not; in fact many Sunni Muslims in the area have most often believed it was their right to rule, as is still the case in the Gulf States ( where Sunni Muslims are the minority) and in Saudi Arabia.
This 700 year Sunni-Shia split in Islam is what keeps resurfacing in Iraq/Mesopotamea local divisions and historically is replayed again and again, with violence until some new balance/accommodation is reached by force or by agreement.
The Ottoman’s kept the peace in Iraq/Mesopotamea the longest by the combination of a lot of local autonomy and assurance the Ottoman rulers would get rid of any opposing their rule. However, to the Shia, it was the later part, acting as suppression of them, by the Sunni Ottoman’s that continued to subjugate them in spite of much local autonomy they often had.
Yes, the Kurds have always been a separate people joined by force of the governing power into rule by a common central governor that was never a Kurd and almost always an Arab or Turk Sunni. That is not new to the modern state of Iraq.