No one’s disputing that legacies have an advantage, but I think it’s different from what you think it is, @observer12, and varies very substantially depending on who a legacy is.
The baseline advantage that all legacies have is that because the ~800-~1,000 legacy apps per year at each of HYPS are flagged at the outset for specific review, they don’t get lost among the ~30k or more apps that these schools get every year. That’s not insignificant; it means that a legacy app isn’t going to be read quickly at the end of a long day by a tired adcom and thrown out because it didn’t look special enough at that moment in time to that person.
The second part of the advantage is that, because the vast majority of legacy applicants indisputably meet the minimum academic standards for admission (and many of them are extremely strong), it’s in the clear interest of these schools to admit a not-insignificant number of them (nowadays, a number that translates into ~10-~15% of the class at these schools) - but few enough that (i) there are sufficient spots left for all the other constituencies to be satisfied and (ii) it doesn’t look to the outside world like there’s a hereditary aristocracy.
If alumni felt that their donations and involvement provided no advantage to their academically-qualified kids, those donations and involvement would fall off a cliff, to the university’s significant detriment. So, a fluctuating number of spots roughly equivalent to the number of recruited athletes is, now and for the foreseeable future, loosely reserved for a cherrypicked group of legacies (~70-~80% of legacy applicants are denied at these schools, as we know) based on what they bring to the party.
Which brings us to the often-overlooked fact that legacies are admitted, just like everyone else, on the basis of the entire package, including the aforementioned alumni giving/involvement as well as (which you flagged) where they went to high school and how they did there.
A legacy who attends a garden-variety public high school that sends a couple of students every few years to the legacy school, and whose alumnus parent donates a few hundred dollars a year and maybe occasionally does an alumni interview, enjoys no appreciable advantage beyond the first and second ones I noted, which, in the context of roughly 800-1,000 legacy applicants a year competing for roughly 200 offers at one of these schools, means very little. That kid needs to be a star, highly competitive in the context of the overall applicant pool, to be admitted - especially because their family may not be able to afford the kind of enrichment/test prep, etc., that other legacy families can. Every year, a significant number of such “weakly-connected” legacy stars are admitted at all these schools, and do very well there.
On the other hand, if a legacy applicant attends an elite private high school well-known to the admissions office for its academic standards, and where there is a good rapport between the college counselors and the admissions office because kids are admitted from there every year, and the applicant’s family is highly involved/generous, and the applicant (because he/she attends such a school) has had strong academic preparation and produced a well-developed application, with test scores (possibly bolstered by the tutoring that his/her family can afford) that stack up well against the admitted class, they are going to have a very significant advantage relative to other applicants in the general pool, other applicants with middle-class/affluent parents who have college degrees and, critically, other legacy applicants. That kid doesn’t need to be an absolute star the way the one in the previous paragraph does (but may well be one), and he/she is much more likely to be admitted - and do fine or better than fine in college, by the way.
Ultimately, the real advantage in the game of life, as well as in college admissions, is being born high-SES, to be honest.