“If they don’t have the skills by now to discern the rare genuine achiever from the standard high-pressure, formulaic (or by-the-book, I should say) achiever, then that’s too bad."
“No one - no one at all - has such amazing stats that an admissions committee at HYP will forgive an essay that comes across as arrogant.”
Too late now but I suspect OP would have been much better off applying to Oxbridge where “genuine” talent is absolutely recognized and sought after in the interview, while the application essay and GPA are essentially irrelevant. I know someone whose son was admitted with no formal high school qualifications at all (his parents left him to study math on his own after seventh grade), he just scored one of the top marks on the entrance exam. Indeed my college is happy to indicate that IMO qualifiers are essentially an automatic admit.
Although everyone assumes that Brits prefer to be understated, the corollary is that Americans are presumed to be a bit arrogant and boastful, they just need to be teachable. And it’s more respected by your peers if you can pull off an easy first without much effort than it is if you have to work hard for a top grade (viz the comparisons of Boris Johnson and David Cameron). So I’m quite happy to admit at college reunions that I was a relatively lazy student and spent too much time rowing (especially during my PhD). I suspect that is not something that would go down well at top US institutions, where (from what I’m told) you are supposed to reminisce about how challenging the fire hose of information was.
Amusingly enough I remember the head of college telling us students about Bertrand Russell’s anecdote in his autobiography that he spent his first year in Cambridge trying to find those undergraduates whom he had been assured were the smartest people in the world, before realizing in his second year that he and his friends were them. And he always liked to claim (not quite correctly) that our college had more Nobel Prizes than France because he had won one of them. So I guess even Brits are allowed to have an intellectual superiority complex sometimes.