Our military presence would have been a safety net that reassured Iraqi factions that political disputes would be settled by politics and not extra-legal or violent means--including resisting Iranian pressure. Although I expected our military presence to help fully defeat jihadis beaten but not eradicated while we were there and to deter potential Iranian aggression, these were not my main motivation for wanting us to stay.
And here we see why we needed to stay:
The governor of Iraq's Anbar province in the Sunni heartland said he has asked for and secured U.S. support in the battle against Islamic State militants because opponents of the group may not have the stamina for a long fight.
Ahmed Khalaf al-Dulaimi told Reuters that his request, made during meetings with U.S. diplomats and a senior military officer, included air support for battling the militants who have a tight grip on large parts of Anbar and the north.
The Sunni Arabs--who we defeated in battle and threw out of power, I'll remind you--trust us and not the Shia-dominated government. Even after we left for 2-1/2 years.
Had we stayed (I wanted 25,000 but thought 10,000 could suffice if supported closely from outside Iraq--and when push came to shove would have reluctantly accepted even 3,000, counting on non-military assets--and good luck--to make up for the inadequate number of troops), I don't believe we'd be in the position of also needing to provide direct air support for the Iraqi forces.
But what is done is done. The important thing is that our absence has not made it too late to work the problem and recover, even if we have to expend more effort to reverse losses than it would have taken to defend our gains.
Let's re-win the Iraq War, shall we?