General intelligence and social intelligence are correlated, which makes discussion difficult. Yale's a good example, though. Applicants need a base level of academic achievement to get in, but it's not actually that high. They didn't even require test scores for the last few years. If that were the main criterion, the whole school would be East Asian. Instead, what matters is marketing yourself. Knowing people, or building a narrative the admissions committee is looking for. Social intelligence.

I completely agree that social skills should be emphasized in school-not to reward the people who are already adept, but to impress on the others that they're the primary determinant of success.