HalTheWise discusses a factor I missed (until I sneakily edited it in, so you may have read the later version that included it):

One very powerful contributor that Scott did not mention is that in many cases schools are directly or indically intentivized to have a low admission rate. US news & world report released the first national college ranking in 1983, and donors and board members at various schools have increasingly been using national rankings performance, which directly includes low admissions rates, as a measure of how well a school is doing.

These rankings and metrics also heavily incentivize having high yield (a large fraction of students that are admitted end up attending) which for a fixed size applicant pool also encourages accepting as few people as possible. This has led to the death of safety schools, because they would rather reject a high performing student than admit them and have them not attend.

These factors might also be a driving force behind the rise of common app, since schools are trying to get as many applicants as possible, even if it hurts the quality of their pool.

kaakitwitaasota points out that consulting is an exception to the "where you go to school doesn't matter" principle:A lot of top firms these days won't even look at you if you didn't go to the "right" college. My mother did her MBA at Northeastern, and recently had lunch with an old classmate who ended up at a top consulting firm. My mother's classmate's résumé would end up in the trash unread these days–Northeastern isn't considered good enough.

So while it's probably true on the macro level that smart kids will do just fine anywhere they end up, there is a subset of extremely prestigious, extremely well-paid jobs which will not even look at you if you didn't get into the right institution at the age of 18–which, in practice, means that the élite are chosen on the basis of who they were at the age of 14-17. When viewed in those terms, it's completely nuts.

I'd heard this before; my impression is that a big part of consulting is having prestigious-looking people tell you what you want to hear. If what they're actually hiring for is prestige rather than competence per se, that could make it a special case