There is a new book describing research that shows that even after four generations, immigrants retain about half of the attitudes of their home countries: https://www.sup.org/books/title/?id=35594.
A fundamental feature of American culture is that it idolizes the “common man.” When you allow elites from other countries to immigrate to the US, you’re importing the cultural elitism from those countries, and destroying American culture in the process.
My family immigrated from Bangladesh to northern Virginia in 1989. When I was growing up, it was an egalitarian, decent place. But we were a wave of elite immigrants, and now 30 years later it’s unrecognizable. Much wealthier, sure. There’s tech jobs and elite immigrants to fill them. But the culture has changed completely. And what’s the upside for the people who were already there? Do they really benefit from Google employees pricing them out of housing, etc?
Absolutely not! We need people in position to make decisions to see the world and understand it, not be insular nationalists because they know no other country. We need more people high up in government who are familiar with the mainstream ideas and cultural quirks of other countries, and we need more contact between cultures. Having people go to other countries is vital.
You also want enough of them to come back home, ideally (though not all of them, expats are still useful from a soft power point of view), but keeping them and preventing them from going abroad in the first place is really bad and counter-productive.