Maybe the reason why the West hasn't been conquered by Muslim fundamentalists yet is that Muslims don't have an equivalent of Genghis Khan. Someone who would have the courage to conquer the nearest territory, kill horribly everyone who opposed them, let live those who didn't (and make this fact publicly known), take some men and weapons from the conquered territory and use them to attack the next territory immediately, et cetera, spreading like a wildfire.

"Caliph" Abu Bakr al-Baghdadi and his group ISIS have been behaving exactly like this. They are quite young, but don't appear quite able to take on a Western military yet.

This feels to me like a just world fallacy, or perhaps choosing the most convenient world.

And yet, by definition, a group who are better at rationality win more often. We ought to expect that rational civilizations can beat irrational ones, because rationality is systematized cross-domain winning.