Based on my experience from my high school Harvard and Stanford accepted only kids that were truly and utterly brilliant and would occasionally make an exception only for scions of political dynasties or very rich families. I went to a rather tony prep school outside the US so I can only talk about that kind of environment. Harvard and Stanford admitted only the truly brilliant kids. Not more than 1-2 per year. These kids were pointy but not too pointy. They had obviously perfect grades and scores. One of them was an international math Olympiad champion, a chess champion and a very accomplished pianist. Another was a debate world champion and a math & physics Olympiad champion.
An interesting observation was that there was a big divide in the quality of students heading to Harvard, Stanford (and also MIT) vs the other ivies and top schools (even Yale,Princeton). The other ivies would accept very smart, motivated and accomplished students but these students didn’t not have the wow factor that the Harvard/Stanford-bound students had. At least that was my observation at my high school which might not be true everywhere.