If we put the "religious right" in charge of drafting a new constitution for the United States, do you think that maybe they'd want one a bit more overtly religious than the one we have now? Maybe one that specifically said abortion was illegal, prayer was okay in schools & other public places, same sex marriage and sexual immorality were illegal, etc.?
I'm not saying that having Islamic law enshrined in the Iraqi constitution is a good thing; from what I've seen it's not that compatible with human rights. HOWEVER, if you have at least a third of the drafters who are very religious, and that is their religion, I don't know how you would expect anything else -- unless maybe we just spelled it all out for them and made them take what we wanted them to have.
We made Japan take what we wanted them to have.
Seemed to work just fine with them.