Sandel's position is somewhat different. Been a while since I've read the book, but as recall it he said that admissions should involve two phases. The screening stage would eliminate the least qualified candidates, basically the people who are not going to be able to do classwork. I don't think he gave any numbers but he estimated that the percentage wasn't that large. Most of the applications are based in reality and therefore most of the applicants have a pretty good idea about their own capabilities. The lottery would start with the pool of qualified applicants.
It got more complicated when he started dealing with other aspects of admissions policy, especially the degree to which a university wants future graduates to have different demographic characteristics than previous graduates. I remember one idea was to give some categories extra tickets in the lottery to tilt the odds in favor of desired changes. Not to deny admissions to any specific person, but to sometimes give more chances to other kinds of people.
(He covered some of the same material in a later book. Which reminds me that it's probably time for me to check what else he's written lately. I've read a number of his books and found all of them interesting.)