I think Turkey's population is more secular than Iraq's Shia, too. I don't believe the Sunnis are as worried about Islamic law, but again, I could be mistaken.
We made Japan take what we wanted them to have. Seemed to work just fine with them.
It appears to me that there are two differences here. Again, I'm not involved with the process, so I'm stating my opinion based on what I've seen.
It seems to me that in Japan, we were more inclined to want revenge, and less inclined to worry about the perception of the "democratic process" or about getting on out of there.
In Iraq, we seem to want it to at least appear that this is an Iraqi democratic process, which means they have to have some say in it.
AND, we seem to want it done ON TIME above all else, because the administration, the media, or both seem to think that every delay is a failure, and also until a new government is fully in place & stable, we can't leave, and a lot of people seem to have expected us to be gone by now. (I personally think that was an unrealistic view.)
Personally I think this attitude is shortsighted, especially given that there's no history of a democratic process in Iraq and it took quite a while for our own country to get it right, but that's the attitude I'm seeing.
We need a presence there like we maintained in Germany after WWII. We need large bases in the center of the Hell that is the Middle East. That is where our demons are coming from.