Getting back to competitiveness, as opposed to just math competitions, I finally found the thread that I read a couple of years ago by someone who had compiled a list of top award winners who enrolled at MIT for the class of 2023.
Naturally, MIT will be very STEM heavy, but it still surprised me just how much world-class talent that it gets to enroll there. By my count, there were 65 unique names listed, and this does not include those who “merely qualified” for something like USAMO, but just the winners and honorable mentions (roughly top 10% of USAMO qualifiers).