It won’t matter at top universities (all the famous brand names, basically).
It WILL matter at all sorts of colleges, from the elites a bit below the super elite (say, Bryn Mawr, Northeastern) to flagships and regional universities. They’ll be put in a torturous bind - less federal grant money, fewer students so less tuition revenue. At the end of the food chain the smallest (especially if 800 students and under) private colleges with a mostly local recruitment base (think: McPherson KS, Davis&Elkins, Elmira, Thiel..) won’t be able to sustain their offerings and will really suffer, creating a domino effect upon their often rural communities.
But Harvard, Stanford, Northwestern, UVA, Williams, Vassar..? No. They’ll still have WAYYY more applicants than places.