I think Iran is playing the same long game it has in Iraq for several years -- really several decades.
So, no, I don't think that Iran has a failed state on its hands. What it had for several years after 2001 was the threat of American-dominated states on both its western and eastern borders. Now it faces no such threat, and is consolidating its hold on the Shiite rump in Iraq, from Baghdad to Basra. That's a big piece of important territory that represents extension of Persian control to the Euphrates, and because that area includes Basra, tighter control of much of the Persian Gulf.
And after Iran finishes there, I think eventually it will turn its attention to the Kurds and get some of the oil up there. But no hurry.