When elite colleges get 15-20 applicants for every student they admit, how would you propose they implement this? Roll a d20, score a critical hit, get into Harvard?
That outcome might be aligned with your goals; it's probably not aligned with Harvard's goals nor that of their alumni.
There’s data to suggest that applying to Harvard is a stronger predictor of lifetime outcomes than the incremental prediction provided by graduating is. So, much of the benefit is provided before campus, but that doesn’t mean that 5x as many people would get the benefit if only they’d be convinced to fill out that application by virtue of admissions being driven by rolling dice.
https://time.com/54342/it-doesnt-matter-where-you-go-to-coll...
That’s basically how it works now anyway.