I think the conferral of a degree is supposed to symbolize more than that, though. An institution's degree asserts some minimum level of education broadly, with an emphasis in the field of study you chose.

I would be cautious about schools that do this. Unless its published that SAT score presence didn't affect chances to get in, I would assume its largely a play to get more applicants to reduce acceptance rate, with no scores counting against you heavily.

Anecdata of 1, but in my grad program, standardized test scores were used to sort students best to worst, and then they were evaluated one by one, given an accept/reject rating until all slots were filled. The score didn't affect your chance of being accepted given you were considered at all, but it did determine the chance of being considered.

But you do need to demonstrate some base level of academic ability.

Part of the issue is that the SAT is not difficult enough to stratify the applicant population, which means that it's not a super useful tool for schools at the very top. The elite liberal arts college I attended liked to brag that they turned away half of the 1600s that applied — and their overall acceptance rate is much higher than H/Y/S.

It would be interesting to think about what would happen if the SAT were more rigorous (or if there were another test that students could take that offered this stratification). Some schools (think Caltech) would probably put a decent amount of weight on such a test. Other schools, who currently optimize for more variables, would presumably not pay much attention.