It is so difficult we still to get a working visa into Western EU. The way this is done is by total bureaucratic nature of Ausländerbehörde.
When he was CTO from Netflix, Gaurav Agarwal Could not get a visa to relocate to Germany. (No more with Netflix)
So even of one has > €80K salary and working in Apple or MS hq in Munich it is pain in the arse.
On the other hand this is encouraging people to apply and get passports. I for one would have never naturalised as German if the residence permit was quick and easy.
In summary, there are encouraging people to migrate.
Many of people I know (or friends of friends/brothers) are migrating from America to either Europe or shifting back to India.
I don't think that America can particularly do something about it. Trust's pretty fragile.