As I was walking to the grocery store:

Ensuring a decent elected government (non-fundamentalist) in Iraq may be as simple as the coalition insisting on two conditions:

That elections be by secret ballot

That women be allowed to vote freely

Half the voting population is female, and relatively sophisticated as Arab nations go. I have no actual survey evidence, but I'd bet the last thing they want, Shiite or not, is to be hauled back into "property" status.

Add to this voting bloc the secularly-oriented males, of which there are more than the negative press articles imply, and the takeover of the fundamentalists may not be as easy as they think.