One oft-repeated trope about Iraq is that Iran and Syria don’t have any interest in an unstable Iraq. Why? While I’m sure that is not their ideal situation, I’m sure that a vibrant pro-Western democracy would be worse in their opinion.
Also the possible strategy of doubling down (a “troop surge”) is doomed to failure. The Iranians and Syrians can trade off lives and money at a very favorable ratio to them for the foreseeable future.
However this is a moot point. Enough highly motivated factions are in Iraq to make the eventual breakup a certainty. What we should be doing is facilitating the breakup instead of denying it.