There's a contrarian theory presented by Robin that people go to highly reputable schools, visit highly reputable hospitals, buy highly reputable brands etc. to affiliate with high status individuals and institutions.
But what would a person who completely didn't care about such affiliations do? Pretty much the same thing. Unless you know a lot about schools, hospitals, and everything else, you're better off simply following prestige as proxy for quality (in addition to price and all the other usual criteria). There's no denying that prestige is better indicator of quality than random chance - the question is - is it the best we can do?
It's possible to come up with alternative measures, which might correlate with quality too, like operation success rates for hospitals, graduation rates for schools etc. But if they really indicated quality that well, wouldn't they be simply included in institution's prestige, and lose their predictive status? The argument is highly analogous to one for efficient market hypothesis (or to some extent with Bayesian beauty contest with schools, as prestige might indicate quality of other students). Very often there are severe faults with alternative measures, like with operation success rates without correcting for patient demographics.
If you postulate that you have better indicator of quality than prestige, you need to do some explaining. Why is it not included in prestige already? I don't propose any magical thinking about prestige, but we shouldn't be as eager to throw it away completely as some seem to be.
I wonder if you could in theory separate out part of the prestige value. Part of the prestige value of a product would be related to its exclusivity - things that are easily got don't confer prestige for obvious reasons.
So suppose you were looking at two schools that were equally prestigous but one was smaller, more expensive, required better social connections and higher academic achievement to access, and was more preferred by people in higher circles than the other. Then you might conclude that this smaller school derived more of its prestige from its exclusivity than the other school did, and hence on other indicators which might matter more, the larger, less exclusive school was actually better.