Yes, Iraq should be divided, and so should a number of other nation-states created by European imperial powers with consequently artificial borders with populations that have proven that they cannot peacefully coexist within the same polity.
Doesn't that presume that the modern nation-state model (one ethnic group to one country) is the only way to organize affairs?
Look at India, with its hundreds of ethnic, linguistic, and religious groups! Surely it's not totally peaceful, but if we followed your example, it'd be divided into several dozen countries. Pakistan would (at least) be split into Punjab, Sindh, Baluchistan, and a new Pashtunistan (with Kashmir perhaps becoming independent as well).
Maybe what is needed is a restoration of the old-fashioned multinational empires. Bring back the Ottomans!