I am fundamentally unprepared to accept the rather trite premise that those people - whoever they are - are incapable of governing themselves without the presence of a strongman.
Ok, so you suggest:
the only chance for stability post-Saddam was to recognize the de-facto partition of Iraq: a Kurdistan (which Turkey was prepared to go to war to prevent), a Sunni more-or-less secular nation, and a Shia theocracy.
Does this not rather admit that "those people" are incapable of governing themselves, full-stop, and need separating?
I'm certainly in favour of your suggestion, though I watch Turkey with interest...