Well, that's certainly what Harvard would argue, although a lot of people might disagree, but even if we accept their/your framing, that doesn't solve the issue. You're throwing around "most qualified" and "elite students" like those are settled terms of art, rather than the heart of contention in an argument that's more than a century old.
Imagine two hypothetical students. One student graduated with a 4.3 by taking advanced courses at a high school where every student gets between a 3.5 and a 4.5 thanks to some combination of intelligence, good funding, grade inflation, and a parent population who can pay for a new wing or two if it means junior will graduate on time. The other student graduated with a 3.8 from an underfunded high school on Chicago's South side, where the average class size was 30+, the textbooks are 20 years old, and the average annual family income is around $30k. Which one of those students is more elite? Which one is more qualified?
Zion Williamson is currently a student and a basketball player at Duke University. He's 6'8", weighs somewhere in the neighborhood of 280 lbs., and a few days ago he had a highlight where he started from under the hoop, sprinted out towards the three point line some 22 feet away, leapt towards a player on that line who was taking a shot, blocked the shot in mid-air, and landed without touching the shooter. The number of people in the United States with that combination of size, speed, and skill is in the single digits. The number of people in the world might - might - be in the triple digits. Is he an elite student? If so, is he more or less elite than the other students in the previous paragraph?
There isn't a clean metric for most qualified or most elite, and there really can't be, because the world doesn't neatly standardize like that. It's a symptom of insufficient consideration of the problem to suggest that fixing a massive and massively flawed system is super simple and just requires One Neat Trick that the thousands of people who have been thinking about and working on this for decades haven't considered.
> There isn't a clean metric for most qualified or most elite, and there really can't be
For an academic institution or an athletic endeavor, I completely disagree. Performance in these environments is measurable. Elite performance is obvious, observable, and measurable.
Should a theoretical elite university basketball team sign and start a 4'11 80lbs person who makes 1% of shots and has only played basketball maybe a half dozen times before total but they happen to be the very best player from their school? What if they're technically the best basketball player in their schools history? Are they therefore an elite basketball player, and an elite performer? I would say no, observably and measurably not.