Wait, what? The nation desired Micahel as its leader? He can't lead shit, he's too stupid for that.
I think the one constant in politics is that a large number of people in any country think whoever's in charge is an idiot and it was stupid that they were even put in charge at all. But this doesn't mean they aren't popular with other portions of that very population. It's less about the truth and more about how they're perceived, that's what gets them popular.
The perception here was that the crown prince was just a cold bastard, while Mil was very warm and perhaps even kind to the common folk in particular. I think he was in that prison tower when he met Elise in this version of events because he stole special alcohol from the emperor and shared it with some random people somewhere. "A real man of the people." If nothing had changed about the public opinion of the crown prince, this might have been enough to keep Michael going as the favorite.