This is really mostly a problem for Japan and Korea where they don't play sufficiently well with immigrants.
Which works for the US, because it's a country of immigrants from all over the place anyway, colonized quite recently in historical terms (there are nations and cultures with 10x and 20x the longevity and far more continuity). If you start with a country with shared history and a cohesive culture, people are not seen as equally replaceable.
What happens to the countries they are emigrating from? Especially if we do as politicians say and "only accept the best", what does that imply happens to the emigrating nation? Are those countries stable then? And are they also now or in the future experiencing population decline? If population growth is due to being poor, is the strategy to keep them poor?
Minority groups have been part of different nations for millenia. So saying "they're not part of the nation" is not a given. They're just not be part of the majority group of a nation. Some nations might not even have such a majority group, but be composed of two or more different groups of roughly equal size. Nations aren't monolithic things. But that doesn't meant they're "anything goes", either.
Nor does "a nation of people is more than just replecable individuals" has "it's OK to exclude and persecute minority groups" as any kind of necessary consequence, anymore so than "this person doesn't belong to my family" means we can mistreat it.
It does however mean that "just bring foreigners in huge numbers to increase the local population" is not exactly a great solution. It might even amount to ethnic cleansing, and this has happened in the past too.
Historical immigration was often part of such power plays and land grabs (like against Aboriginals or Southern Africans), or "population engineering" (those in power bringing in populations to divide and conquer, and to replace and suppress local populations). In fact one of the common targets that was yielded against was exactly minority groups local to a nation or part of an empire.
Immigration at a large scale replaces the culture and race of the locals so what you're suggesting is that Korean people and Korean culture are worth nothing. Let's just make every place on earth a globalist culture with the same people, same language, same brands etc etc. No.
Japan is very easy to emigrate to if you have skills (for many visas defined as an undergrad degree). There is no requirement to hire locally first, the process is streamlined based on a points system it's only a several weeks to get a visa and as little as 1 year to get permanent residency.
It's also easy to go to university there and stay, or emigrate as a low-level blue collar worker. There's a language barrier but for things like immigration, taxes, help in daily life, most cities offer support in 5+ languages. It is missing the lottery system of the US however.
However, if this shortage didn't exist and the economy was humming along just fine without any immigration, these lax immigration laws would not be there. Japan used to be very hard to immigrate to prior to this century.