Iraq under Saddam was in no way, shape, or form a democracy.
Yes it was. It was a defective democracy in which the vote was always rigged and only one candidate from one political party was ever allowed to run. We like to claim it WASN'T a democracy because the means of excluding non-baathists from the ballot was the threat of violence and/or torture and execution.
Just because the system is implemented horribly doesn't change its definition; a defective democracy is still a democracy, just as a capitalist economy that has been dominated by a single gigantic monopoly is still a capitalist economy.
One of the most key ingredients to a democracy is a peaceful transfer of power and FREE elections.
To be sure, that is the ingredient for a SUCCESSFUL democracy, which Iraq was not, and technically, still isn't.
Your idealized system is simply unworkable. One person is always going to be flawed, have their own biases, etc.
Where would the checks on powers come from?
First of all it's not idealized, it's just a matter of statistics. It's easier to assure the benevolence of a single individual than an entire government. The only problem with a dictatorship is the question of HOW you assure that benevolence in the first place and how to remove that dictator if he doesn't measure up. Democracy seeks to accomplish this through elections, but has the added disadvantage that the voters have to thoroughly vet dozens of candidates in dozens of positions to make sure they have the country's best interests at heart, and obviously some of them won't.
But a defective democracy is NOT preferable to an effective dictatorship, just by virtue of their outcomes: ANY government needs to be able to govern effectively in order to maintain order, and even democracy cannot be created in the absence of order. A highly partisan environment with a great deal of social and political strife has to be brought to order first BEFORE a democratic system can be imposed, and the quickest way to do that is with an autocracy.
Let's face it, as a matter of historical truth, NO political system is more effective at maintaining public order than an autocratic police state.
Your philosophy is very similar to authoritarian critiques of democracy, with their emphasis on the maintenance on "orderliness" over the "chaos" of democracy. A creepy idea that's led to a lot of bad results over the years.
And the results speak for themselves, but my point isn't that democracy causes chaos, my point is that democracy cannot function in the PRESENCE of chaos, and that a properly functioning democratic government is ill-equipped to resolve a situation of anarchy.
And this is the case in terms of organized religions, especially protestants and muslims. What we have here is a sort of doctrinal chaos where anyone from anywhere can write their own interpretation of the law and make it legally binding on a small group of followers. Without a strong central authority to overrule them, who's going to stop them? The only one they would possibly listen to is God, who doesn't talk to anyone and basically isn't real; the only human authorities, they reject as illegitimate and go their own way.
An organized religion of the people, by the people and for the people--so to speak--can only be realized when the ENVIRONMENT of the people is relatively orderly and reason is allowed to prevail. You remove central authority in the middle of a war zone, the first thing you should expect is rampant sectarianism and balkanization.