Anyway, when you bring in young single people, the primary cultural diffusion is through their eventual children. They will be Korean in a way that the immigrant parent might never personally feel.
To put it crudely, if South Korea was invaded, the indigenous people genocided and the area colonised by a billion foreigners, I don't think South Koreans would regard that as a boon for their demographics.
Doing this more slowly via immigration is not fundamentally different.
to reduce the NK situation to "they won't let anyone go" is also disingenuous. even if you ignore that the US refuses to allow any more meaningful peace so it can justify a continued military presence halfway across the globe, the US and South Korea are clearly more powerful and wealthy. clearly they are in a better position than NK to make concessions and pave the way for integration.
(Of course South Korea's case is very particular because they actually have an enormous reserve of eager potential immigrants who already speak the language, living just across their land border, an hour away from Seoul. The problem is that the other side of the border won't let anyone go.)