> The whole immigrants who don't integrate seems to be a constant issue in every developed country across the globe

I can't speak for the other countries, but in the US it's almost entirely an agenda being pushed. When I hear people say this, it's not because of any experience they've had, but just a repetition of talking points. Virtually none of them had a negative story to tell. I've heard far, far worse stories in some European countries.

There are notable issues in the Southwest in the United States where people don't speak any English at all, and speak only Spanish, suggesting they are legal citizens born of illegal immigrants, or are still illegal immigrants themselves.