This is a huge dealbreaker for campus hires, and specifically masters/PhDs who are, well, by definition, specialized in their field and hence very rare.
So you recruit at her graduation the girl who has done groundbreaking research in deep neural nets and is the key to one of your big projects. She happens to be non-American (because the majority of graduates are non-Americans).
Now what? You know that there is nobody else on the planet that has done this research, yet you have to start recruiting for this position for Americans.
What is the incentive you have as a company to pour a ton of resources on this effort? Recruiting is very expensive. Time is also very expensive when you are at the forefront of innovation.