I'd counter that the populace at large adores Twilight, mainly by virtue of her being a princess, and I highly doubt they'd instantly turn on someone who has Celestia's (their beloved ruler's) direct blessing. If Twilight were to run the country poorly, then we might be in for some problems. But there's no evidence that that happened. Because the show has suggested many times that when Twilight is calm and collected she's a tremendous leader.
It just seems weird to bring up real world monarchies when I'm fairly sure an immortal person has never been a monarch. So the system being different from our world doesn't seem that farfetched to me.