And if you mean them getting spots in the more prestigious institutions, well, it's not clear whether that will even happen (the few thousand international students admitted to the top universities are not the ones that are likely to decline their acceptance letters), but even if it did, well, those universities are simply not as prestigious anymore.
Attracting the best talent from anywhere in the world is a huge part of what created their prestige, and that's even before we get to how they're losing funding, and professors and researchers to other countries.