When a person migrates, I would believe that the origin country has one less population. So why is it good that this person props up population in the destination country instead of in the origin country?
And why does the destination country need that persons labour and expertise, but not the origin country?
If the native population is becoming exterminated with or without migration, what exactly is the "country" that needs to be kept "afloat"? Your stock portfolio? Your treasury bills? Your real estate investment?
It’s definitely a possibility that a country dwindles away and is happy to do so in order to avoid immigration. We’ll probably see that with Japan and South Korea by the end of this century.
Ultimately it’s their choice.
Whether a country with high population composed of immigration is still the same country we can look to the Americas. Countries with extreme high degree of immigration and assimilation, yet still very much worthwhile countries. Maybe not the countries the natives from 500 years ago would have imagined, but their culture has survived more than 100 years and contribute significantly to the world still. New Zealand is also a good example of native culture not being wiped out even with assimilation.