> And this is despite billions of welfare money given for housing, free education, free access to health, etc.

This assumes those things help one integrate. The Unites States notably doesn't have these things to the same degree that countries in Europe do. This means immigrants in America need to work. And work is a strong forcing function for socialization and integration.

> You mentioned Gypsies, well I read scholarly work stating that they were warmly welcomed 4 centuries ago in the towns of my region, until people discovered a tendency of their purses to disappear.

Do you have a citation for that?