First of all, the US does not have a monopoly of good schools. Europe has many good schools, and there are schools that provide competent college-level education all over the world. Closing the doors of US universities merely directs the demand to these other good schools, and would probably not substantially decrease the creation of competition.
Secondly, the US has a moral obligation to many countries, having terribly damaged their institutions and infrastructures over years of intervention. Even if the US was paying for their education (and we are generally not), a person with a sense of history might not think it's so unfair. One could even argue that the richest country in the history of the world has an obligation to humankind to help develop as much of the limited pool of talent we have. Would it really benefit us if the next Darwin or Einstein is denied the best education?
Thirdly, many universities are private and most professors (except perhaps ones with truly sensitive expertise like nuclear engineering) are mobile. Countries are not going to stop trying to compete with the US just because we stop issuing student visas. If we leave them no other choice, they'll simply invite our universities to set up satellite campuses, or just hire away professors. The resulting brain drain could be even worse.
Basically, the only way it'll work out as the submitter imagines is when there are lots of qualified and motivated US students who can afford the education to fill the slots vacated by foreigners. With the economy in trouble and government slashing education spending, it's more likely that a lot of schools will downsize, shut down, or simply move.