What these discussions tend to elide is the effect of immigration on culture.
Thomas Jefferson wrote that immigration from Spain and Portugal must be carefully limited. Spaniards and Portuguese, he said, came from societies in which both government and religion were top-down, and so they were not prepared for republicanism. While a limited number of such people could be assimilated, he concluded, if too many were allowed to immigrate, it was America that would be changed, not the immigrants.
I think that as usual, Jefferson was on to something. Exhibit A: today’s California.