Wow. The amount of quasi-xenophobic comments in this tread is nuts. They are also a bit misguided.
You don't hire a professor at a R1 school just to teach math101. You hire them they can build a research lab or otherwise help to advance the frontier of the field (cancer, stats, etc.). The talent pool in several of these fields is very very small for Americans, because the brightest just go (used to go?) to work to finance or tech. So if you say you can't bring any bright foreigners, you are constraining yourself to a lower talent pool than other countries, and thus will pay a price (in less research, in no foreign students applying and thus no $$ from them, etc etc)
There's different visa's for gifted people to come into the US. The H1B is not intended for this purpose you claim. The brightest won't be affected by this.
If you are in early career (i.e. graduated your PhD within the last 5 years) you are extremely unlikely to get the gifted people visa. The standard approach is to just get the H1B (not the lottery stuff for tech companies but the non-lottery one for hiring faculty at universities). Ask any foreign MIT professor hired early in his career and they went through H1B (and later on, they are more reluctant to move into a place like Florida..)
You don't hire a professor at a R1 school just to teach math101. You hire them they can build a research lab or otherwise help to advance the frontier of the field (cancer, stats, etc.). The talent pool in several of these fields is very very small for Americans, because the brightest just go (used to go?) to work to finance or tech. So if you say you can't bring any bright foreigners, you are constraining yourself to a lower talent pool than other countries, and thus will pay a price (in less research, in no foreign students applying and thus no $$ from them, etc etc)