Oh geesh.
These people are Muslims.
Muslims have a habit of injecting their religion into any government they form. It is inevitable. Even an officially secular state like Turkey can't get away from it. That's the way things are.
Frankly, I don't give a rat's patoot what kind of government they end up with as long as they no longer sponsor terrorism against the West, as Saddam did.
It's still drivel.
I agree with you, however, we should be very concerned about the possibility of Iraq becoming more or less an extended client state of Iran. Iran is one of the biggest state sponsors of terrorism in the world after all, which I think is why they were included as a member of the Axis of Evil, and rightly so.
If that ends up happening, the situation might well end up being as bad or worse than it was before. An eventual showdown of some kind or another with Iran seems inevitable.