The classical liberalism of the nineteenth century was a sustained attack on unearned social status. The old nobility and the established church were fitting targets for this attack.
Today's classical liberals may or may not follow the same path, but the best among them know that unearned social status and special privilege are harmful formations that can reappear again and again in all kinds of societies. It is good that in the United States, birthright citizenship prevents a permanent lower social class from emerging. Even those who cannot get citizenship can see their children will get it, and this ties them to the polity, and brings their interests into alignment with those of the citizens.
The article argues that we should look to citizenship as one source of social distinctions that is not always properly founded.
Remember, people seem to have a need to belong to a group that is bigger than their neighbourhood but smaller than the world. National, ethnic, or racial identity is that group for many people. It provides a sense for belonging. Good luck getting a long established nation like China, Korea, or Japan to disband itself.
Citizenship obviously covers a much wider percentage of people. Assuming for the sake of argument that it is equivalent to hereditary aristocracy, it’s going to be much more difficult to attack. The number of true cosmopolitans that want countries to be nothing more than an administrative subdivision are as few as the problems with internal migration within the European Union.