That's a problem of attitude, not genetics. A person born in Korea can become American, British, Swedish, Singaporean, Brazilian, etc. There's no fundamental reason why it wouldn't work the other way if Koreans wanted their society to be open to newcomers. With shrinking population they may want to have that national conversation eventually.

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.

I'm quite sure that South Koreans aren't so much concerned about the declining number of people occupying the area within the arbitrary geographical border known as "South Korea" so much as they are concerned about the declining number of ethnic South Koreans.

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.

It's entirely different if the newcomers are primarily young and single and start families with non-immigrant Koreans. Seeing that as problematic is a slippery slope into Nazi-style racial heritage mathematics where you'd be obsessing over who's only 3/8 Korean, etc.

We'll have to disagree there. I'd much rather be called names than be complicit in the demographic replacement and genocide of my people. I'd even argue that crossbreeding would be more catastrophic for the South Korean ethnicity than population decline. The latter is recoverable as the stock of the nation remains intact, while the former permanently alters the genotype of the population - even if the numbers recover, this is not fundamentally the same people as those who existed before.