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.
Where does the prestige come from? Likely, it's got a lot to do with public perception of quality in the first place. If we can improve objectivity in the judgment of this quality, then that's great; but the prestige would follow it along. We won't 'do better' than following the prestige, the prestige will 'do better' at following the quality.
The usual assumption is that public perception of quality is systematically biased and that individuals willing to do better shouldn't automatically agree with it. It's not a given that good indicators of quality known to experts are widely accepted. This post presents a hypothesis that public perception may be a pretty good indicator, incorporating other indicators as they become known.