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.