Kim Jong-un is an irresponsible madman who should not be in charge of any country. He is not qualified to run the country, but he only came to power because he is the son of the former leader. His provocative execution of his own uncle has shown just how erratic he can be.
If it wasn't clear already, the Kim family or dynasty or whatever you want to call it is filled with insane people. Literally insane people. We're not just talking power-mad dictators. At this point, it's unclear what North Korea's endgame is other than the complete internal collapse of their state. Holding out as long they do is just going to make the inevitable process of cleaning up and democraticizing the state that much more difficult.
Kim Jong-un shouldn't be the leader of North Korea because he's ruining his country's people. Just like his father, Kim Jong-un is a despotic idiot who is all about lining his own pockets and trying to get nuclear weapons. Unfortunately, the people are too poor and too hungry to try to overthrow him or the military. It's going to take a group of military leaders to gang up and get rid of Kim.
No, Ki Jong-un should not be the head of politics in North Korea, because he has a terrible human rights record. John-un isn't even above killing his own relatives whenever it suits him. More diverse and open leadership that turns around every once in a while would do a great deal of good opening North Korea up and making it a stable place to live.
No, Kim Jong-un should not be the head of anything. He's a dictator, essentially a hereditary monarch in Communist clothing. He's also about five different kinds of crazy, as well. That general he suspected of treason? Not only did he have him executed, he killed his entire extended family as well. They need a regime change there.