Huh? In general they do — either the SAT or the ACT. Only a few big universities don't require them (though COVID has led many/most to change their policies at least temporarily).
In other countries, though, the admissions exams are much more heavily weighted. Here they play a minor role. No one is getting into Harvard on the basis of a perfect SAT score, and plenty of people get in on more than a standard deviation below a perfect score.
Minor role is unfair. It's more like a good score is necessary but not sufficient. Basically, you can have a perfect SAT score and GPA from high school but you have no hobbies or other interests than studying and your essays are unimaginative, you're probably not getting admitted.
But you do need to demonstrate some base level of academic ability.
Well, you can also have a perfect SAT and GPA and lots of interesting hobbies and extracurricular successes, but then get rejected in favor of other applicants with significantly weaker applications simply because subjective evaluations, under the direction of admissions offices, tend to claim that people of your racial background are all unimaginative drones...
You're right that a perfect SAT isn't a guarantee of success, although anyone who nails the SAT will be admitted to a pretty good school (assuming their GPA is commensurate).
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.