Having to arrange separate transportation home because you stayed after school past when the buses leave is also a cost.
But elite schools select for (1) students who will enrich the experience for their classmates and (2) who are likely to have an outsized impact on the world as adults and bring prestige to the institution.
There are some people who are so quantitatively intelligent that a lack of social skills/intelligence doesn't matter (geniuses), but these people are so exceptional they can't be really measured by a test like the SAT. It's too easy to get a perfect score.
Instead they'll distinguish themselves by excelling at STEM competitions (eg. Math Olympiad, programming contests, the Putnam).