This is why I wrote in another comment that making it about Harvard somewhat muddies the discussion because Harvard probably is more likely to admit at least a slice of students that are far more about pedigree than anything else.
But as you say, you need to not only have the credentials, something else that sets you apart, and even then the Teela Brown luck gene. When you're being that selective, there's no way that you're realistically finding strong signals in all but the most exceptional circumstances to admit specific individuals.
(And things have only gotten more competitive. I would be shocked if I would get into my undergrad school today.)
There's a great Veritasium video about this. The idea is that if there are far more applicants than positions, then even if luck plays a small role - say, 5% of the outcome - successful applicants are overwhelmingly likely to be extremely lucky as well as highly qualified. Since so many people are close to that 95% competence factor, only the luckiest - by whatever metric of "luck" you like - can succeed.
They probably reject way more than 50% of the valedictorian/800 SAT applicants they have.
Unless you are super-special, you need to be at that level and be lucky