And I'm highlighting that while a drawback might have existed, it may not be as relevant today. I can see why a Romanian would move to Paris after Romania entered the EU, but the advantage today seems fuzzier.

The areas of large population growth in the USA, mainly driven by internal migration, aren't the rich cities. Instead, they are cities that offer cheaper quality of life, attracting people who can effectively see their material wealth increase even if they don't earn as high a wage.