[diminoten]

Fairer? Yes. Better? No.

The college application process screens for more than just measured ability, and forcing colleges to take on people who aren't a good culture fit changes the experience at that college for the worse.

[nradov]

It may change the culture at some schools. Whether that would be better or worse remains an open question.

[albntomat0]

Many of the Ivies admit that they have multiple freshmen classes worth of qualified applicants every year.

The lottery doesn't mean everyone who applies gets the exact same chance. It could choose among the qualified, perhaps using some sort of weighted system.