> You can't really expect a company hiring PhD's in a niche field to show that they couldn't have spent 7 years training an American for the work

I don't believe for even an instant that there is a significant amount of immigration happening to bring in people who are that specialized

Some, maybe. But not the vast majority of it

My former employer exclusively brought in that kind of talent.

But it was so hard to get the visas (and so much uncertainty in whether or not they'd be able to secure a visa for any particular worker) that they opened up a European and Canadian offices.