Then the freshman class is simply selected by choosing the number of available spots by random from those who have passed the threshold and entered the lottery.
It seems this would take a lot of pressure off high school students since meeting this threshold would be a well-defined goal. Once they've met it, they can start investing their time, energy, and resources into other pursuits like passion projects or time with friends, which would be a boon to mental health.
And the admissions process is essentially random anyway for the elite colleges, assuming you have sufficiently high scores. Making it explicitly random would take some (perhaps undeserved) prestige, status, and exclusivity away from the degrees from these schools -- not that the schools aren't good, or that it isn't hard to get in, but that there are many more who are just as well qualified that do not as there are who do; a fact that would be more well-recognized in society if the lottery approach were adopted. Of course, the elite schools don't want their status (and therefore degree value) tarnished so we're unlikely to see this happen of their own accord.