> If that is their goal, should they even be classified as a university?
There is no universal definition of what the goal of a university should be.
At the very top of Harvard's mission page it says, "Our mission to educate future leaders is woven throughout the Harvard College experience, inspiring every member of our community to strive toward a more just, fair, and promising world."
There is NOWHERE where they say anything even remotely like, "Our goal is to reward students who do well in high school coursework and testing." Nor do they say anything like, "The mission of Harvard is to teach as much academic material to students as possible."
In contrast Caltech says, "The mission of the California Institute of Technology is to expand human knowledge and benefit society through research integrated with education. We investigate the most challenging, fundamental problems in science and technology in a singularly collegial, interdisciplinary atmosphere, while educating outstanding students to become creative members of society."
It's much more focused on solving science and tech problems and a focus on educating outstanding students. There is very little here about leadership.
And so you tend to see that CalTech has some of the top scientists and professors in the world. At the same time, even in tech/science companies, they occupy a small percentage of CEOs. Those aren't the people they are intending to nurture.
There's room for different types of education with different goals and metrics, including admissions metrics.
And anyone can create a university and say,"We look at grades and test score. We don't ask for recs or essays. Don't care about what your goals are. We stack rank based on GPASATAPs and then select the top N." That's a perfectly valid approach. I wouldn't want to go to that school, but it sounds like there are some students who would, and I wouldn't object to it.