I guess the competing affinities here are nationalism versus religion. I can see the Shia government in Baghdad deciding they are going to be happier without the (mostly Sunni and decidedly not Iraqi) Kurds.

Neither side has much of an identification with an Iraqi identity. The Kurds have their own strong sense of Kurdishness, and I think the Shia feel like their creed is more important then their country.

If it's ever going to happen, this might be the time.