The Wikipedia article you linked actually links a source which attempts to explain it a bit:
It is a 6-month extension of the previous ban that was scheduled to end Jan. 31.
The move was aimed at protecting South Korean people's lives and property from those countries and regions suffering political instability, frequent terror threats and poor security infrastructure, the ministry said.
Above and beyond that, there's some interesting reading in the others that might provide additional speculation points, if anyone is interested.
For example, the US bans entry into North Korea because "They also threatened U.S. citizens with being treated in accordance with the “wartime law” of the DPRK" despite us not actually being at war.
Several cases are simply because one of the involved countries doesn't recognize the sovereignty of the other state (namely Israel and Palestine), so it's a technical issue and if you show up there, you'll be treated as if you showed up with a fake passport. I can think of reasons why those countries would ban travel of their citizens in those cases, above and beyond a warning.
The UK government has had phenomenal pressure to intervene in the case of the teenager who was arrested and charged with making a false statement about being gang raped in Cyprus. That case has received international attention and has certainly cost taxpayers in dealing with it.
The US government reportedly had to sign an agreement to pay $2m USD for the care of Otto Warmbier's care after he went into a coma while being held in a North Korean prison for stealing a poster from his hotel (he was charged with Subversion). The White House denies paying this bill.
As you can see, while only a brief, vague official reason was given, there are plenty of causes where if significant friction between two states exists, banning, rather than simply warning, might merit consideration. Diplomatic incidents can worsen already stressed relationships and cost the involved states a significant amount of money under public pressure to safeguard citizens overseas, even if a warning was in place beforehand.