If you think islam is a religion, as most people do, then yes you are right - you'll be frustrated hoping for a muslim democracy and wondering why there can't be a separation of church and state in the western mode. If however you believe islam is nothing but an imperialistic political movement (which is what I believe), then it comes no surprise at all that there are no democratic muslim nations, or that it is not a "religion" of "peace".
The death squads of the sectarian violence are not the same as the insurgency. But a sovereign Iraqi government with the rule of law must clamp down on them just the same.