Several 5th Group retired NCO’s told me a few years before the Iraq War started they had trained with the Kurds before Hussein came after the Kurds the last time with chemicals etc. Your diversity sounds OK, but; the Shiites damn sure did not mess with Saddam Hussein. He ran that country just like Muammar Gadaffi did Libya. Those two dictators worked much better then we have now. My opinion.
I heard the same thing, but my point is not that the Iraq needs diversity...it needs LESS diversity and more unity by ethnic group, in my opinion.