Grossly, south korean couples each makes 1 child. So its population is going 1/2. To correct that and return to previous level, every couple formed among those children would have to bear 4 children.
I think they won't and it looks grim.
Calculating the carrying capacity of the world before agriculture would have given you a much different number than after it.
By that logic we shouldn't be applying arguments like "It is quite normal in ecology to see crashes and recovery in the event of overpopulation".
It is not blind faith to say that we should expect that the different dynamics could be different when the rules of the game are different.
Again, if the foxes see the rabbit population declining and can start producing rabbit substitute before they start starving, of course we would expect a different dynamic to be possible.
“Carrying capacity” is a technical term that implies, among other things, that no further population growth can occur.
It doesn’t just mean “too many” or “more than we’d prefer”.
Well look at the bright side of your unrealistic South Korea extinction scenario; no more DMZ and North Koreans will spread southward!
Of course this will never happen, there is no likely scenario for South Korea to have zero inhabitants. Y'all are High-larious.