Is "valedictorian" a good signal? I'm from Europe so we don't have the concept, but it seems to me that being the exact single topmost student in a cohort would set a perverse incentive to game the rules and hyperfocus on getting this label. To me being somewhere in the top 5%-10% while ignoring some bullshit and not caring about maximizing all grades would indicate a more robust mind that is focused on better priorities. (I'm not claiming it is easy to become valedictorian, I'm just wondering what precisely it indicates about a person, besides obvious talent and conscientiousness etc)

This is anecdotal, however I remember hearing about farmers trying to maximize for egg production. Multiple hens would share a cage. The initial criteria was to only breed the hen that produced the most eggs. Overall egg production declined though. It turns out that the best performing hen was doing so at the cost of the others, ie. eating more than its fair share, being combative. The strategy that worked in raising overall egg production was breeding all the hens from the best performing cage.

It's a no-signal or slightly-positive signal until paired with other signals.

For example, doing it at Columbia is meaningful. Doing it at a random school, not so much.