@CronosusCZ because he's got heart! And that's what's important in a manga like this, eh?
Remember: once he's king, since he's not a bad person, he's got his brothers and sisters and new wife to help him. Because none of them want the crown, none of them are a threat to the nation, and he can use his authority to get them to act as his smarts and his might. Particular 5th Sister will be looking out for the nation (and his) interests with her smarts.
But it's a cute sweet manga, it doesn't need to make that much sense!
Truth to be told, it's not a cute sweet manga that doesn't need to make sense.....it's so stupid it actually hurts
Plus, i completely agree with Cronosus: why making someone so dumb the king? Seems to me that the father is even more stupid and more willing to leave the throne than his sons...