A 1600 vs 1580 SAT or 36 vs 35 ACT is not a good basis for discriminating between brilliant (say top <0.1%) and very good but not brilliant applicants, especially given how teachable those tests are. You need a much longer tail test than that, something like the AIME or equivalent. Or at the very least you’d need to administer a single sitting SAT with no prep that was recentered to lower scores (which is much closer to how the SAT testing was done 30 years ago). The alternative would be an Oxbridge-style academic interview of qualified candidates, but that’s not what US interviews are designed to accomplish (or in general the aim of the US admissions process, as others have noted).