Actually Chamberlains replacement is responsible in large part for the mess we inherited. We just made sure the fire is stoked. When an entire region is bombed and their people thrown into chaos by foreign powers for no fault of their own, they tend to resent those who came in and did more damage than any terrorist did to the west. There was no right time to leave. Iraq will never be anything more than it is until we leave and people there work things out any more than the Brits should just have stayed in America and we'd be loyal subjects if they just stay and kill enough of us, and the people in that region think of us just like we did the British and for the same reasons.
Yeah we already know your official position is to let the fire burn itself out.
The problem is that fires do not always burn themselves out fast enough or stay confined. Local fires can trigger much larger fires, as any historian knows. Look at how WWI started for instance.
If the US had NOT intervened last year, it's possible, even probable, that ISIL would control virtually all of Syria and most of Iraq very quickly. The sneak attack into Erbil would decapitate the Kurdish resistance, and Kobane would have fallen in weeks without air support. Baghdad itself would be too hard to take, but they could sweep the oil fields to the south and east and from there, not only in Iraq but also Kuwait, and incite riots in Saudi Arabia and drive oil prices to crippling highs.
Saudi Arabia is fundamentalist, so they'd have a Fifth Column. If ISIL took Mecca/Medina it's hard to see where the snowball would end. The rest of the peninsula would be overrun soon after, and the loss of Saudi support would further destabilize Egypt and Libya, which benefit greatly from Saudi oil money.
At some point in all of this Iran might try to openly send its army to recapture territory outside of the SE territories, but that would draw even more idiots from around the world to what would be an even bigger sectarian war and possibly drag Turkey directly into the mess as well if those "Shiite militias" (read: Iranian puppets) kept slaughtering Sunnis indiscriminately. Turkey's prez is insane so don't put it past him, he thinks he's Defender of Islam or something and even had people dress up in Ottoman garb to welcome guests to the massive palace he built for himself. While claming Muslims discovered America, among other things.
If ISIL got strong enough with so many countries and oilfields under their belt, they might attack Turkey directly to annex it as part of "fulfilling the Dabiq prophecy" on their way to Rome.
Turkey is a NATO country (I wish it weren't) so it would spiral out of control at that point.
ISIL also has sympathizers in Pakistan, which itself unstable. Imagine ISIL getting its hands on some Pakistan nukes during a Pakistan civil war.
Would this necessarily happen? No. But it's one of many possible nightmare scenarios. You seem to think ISIL is some sort of campfire that will burn itself out, when it's more like a brushfire uncomfortably near a bunch of extra-dry forests in late August.