Interestingly, one reason the U.S. doesn’t accept a lot of immigrants from Europe is that those governments have quietly been putting pressure on us for decades to restrict immigration for their people. They’ve long been fearful of a “brain drain” where their best and brightest leave and come over here.
Probably a reasonable concern on the part of European countries!
One of the other problems has been US unions. I have had several friends, both British and Spanish, who have tried to emigrate to the US or even simply work here briefly in the teaching field. The problem is that they were better qualified than our own teachers, and thus were in demand by school districts, so the union response was to put pressure on the federal government to restrict the number of European teachers who could be accepted here.