Opinions about a Prestigious University Admitting Some % of Students Randomly

Considering what college admissions in the US has turned into today, I've wondered for a few years whether a prestigious university could benefit by specifying that 5 or 10 percent of students would be choosen at random if meeting some basic standard like a 600 average SAT score and successfully graduating high school.

I think it would give opportunities to those who are less traditionally qualified and have an additional benefit of adding a seed of doubt to many highly qualified first years that maybe they had gotten randomly rather than "earning" their spot.

It would also acknowledge the fact that places like ivy league schools get as much as 20% of qualified applicants but accept much fewer than that, making admission, for many, essentially a lottery, rather than something they've earned.