Yes, they do. It's called the H-1B visa. Lawyers, accountants, financial analysts, physicians, surgeons, management consultants, architects, journalists, school teachers, nurses and many other occupations qualify for H-1B visas.
One ref: https://www.bostonglobe.com/opinion/2014/05/09/the-lawyer-bu...
The “bar” is not representative at all of the nature of the work is why. It’s artificially high in order to eliminate a glut of candidates early in the process.
I remember when there was a genuine shortage of tech workers - the dotcom boom. Hiring and compensation reflected that there was high demand and competition to hire. Outside of a very few niches now, the economics (law of supply and demand) simply don’t show it.
Undergrads (not me though) can make $225k out of school now easily, is that not showing it?
If there was genuinely a shortage of tech workers there would be no ageism (or any other sort of -ism) nor would there be these elaborate multi-day hoop-jumping interviews.