For example, assuming Harvard is mostly a status symbol, if that became common knowledge, how much would the quality of its applicants drop?
It's a stretch of the vocabulary, but Harvard and other elite institutions are a Schelling Point. Those with status send their kids there, because other people with status do so. Therefore, even if it were proven that the Harvatd education was equivalent to an average California State College, the nexus of networking opportunity would still give it significantly enhanced value.
If that were true, and it became common knowledge (universal expectation that everyone else believes it), it would likely reduce the number of people willing to pay that much by quite a bit.
It's probably not true (it's one component of value, but likely not the majority), and there's a lot of emotional investment in not believing it even if it were. so I suspect this is not a world we'll find ourselves in.