This considers only academic knowledge, and specifically only that knowledge that can be assessed in a standardized way.
Such knowledge makes up a very small fraction of success -- though you could make the argument that students' ability to acquire and demonstrate it probably correlates with success much more than the knowledge itself.
Second, why would you want to go to college with a bunch of other kids who just meet some bar on some measure of academic capability? At least in the US, college is most kids' first experience living away from home for an extended period of time. Wouldn't you want to be with driven individuals, interesting conversationalists, performers, intellectual peers across other disciplines, etc.?
Why limit admissions to "book smarts"? Why is that the most fair?
As such, in a university setting, I expect to be surrounded by people who are curious, who value learning, who are building up the skills and knowledge to excel in their chosen fields. In my own country, universities are usually specialized, and further divided into highly specialized 'faculties', which has upsides but also downsides. Still, even in the American college system, I would expect all of my peers to be interested in excelling in their chosen fields of study, whether that is music or sports or medicine or computer science. I would not expect to be surrounded by people who are just ok at academic knowledge but are really driven social workers, or by people who have basic knowledge in a lot of fields, but no advanced knowledge at all.
Do you truly believe you can measure this with a single standardized exam?
I’m not even sure you can measure academic knowledge with a standardized exam, let alone all the other attributes we agree we’d like to see in peers at university.
One thing is for certain: the SAT is not that exam.
In the end, there isn't any point in admitting a student to a university where they don't understand the curriculum. So the important question that I expect universities to ask themselves is: are we getting enough information about how well a student is going to be prepared for our curriculum based on their SAT score?
If rich people who know less have higher SAT scores than poor people who know more, then the systemic bias is in the SAT itself. If not, then the SAT isn't the problem, the actual school system is. And, unless they want to take on educating younger children, Universities can't to do too much to fight that type of bias.
I firmly believe that exams are in principle the only fair way to do admissions in educational institutions. They could be national exams or admissions exams created by that institution itself, but either way, as long as the exams are kept un-biased (which I'm not claiming is an easy problem to solve) and scoring is anonymous, you get the closest thing we have to a fair process.
The only alternative could be an easy exam covering just the bare-minimum knowledge, and a lottery system for everyone who passes the exam.
Of course, private universities are free to be as biased as they want. I don't think it's ethically or morally correct, but it shouldn't be illegal.