Suppose that the stats you listed are accurate – 7% of students attend private HSs, and 35% of selective private university undergrads attended private HSs. This does not prove that “the boost that a student gets from legacy admission pales in comparison to the boost they get for attending private high schools.”
One also needs to consider things like differences in portion of kids who apply to selective private colleges. Kids who attend selective, private HSs tend to apply to selective, private colleges. Kids who attend typical, non-selective, public HSs tend to apply to typical public colleges. For example, I attended a typical, non-selective public HS in upstate NY. The vast majority of kids from my HS either applied to SUNYs or one of the nearest community colleges. A significant portion of the highest achieving kids applied to and attended a SUNY. I expect that is still true today with the SUNY Excelsior scholarship covering tuition costs. I know some who started at community college as well, usually to save money. Only a very small portion of students applied to HYPSM…, and very few were accepted to HYPSM… However, a good portion did apply to the upstate NY college Cornell, and we had a good number of matriculating students to Cornell each year. This is a very different pattern of college applications than occurs at typical private HSs, so a very different pattern of college matriculations are expected than at typical private HSs.
Another important factor is the concentration of kids who would be well qualified applicants for highly selective private colleges. Private HSs usually have a much higher concentration of such students than public HSs, particularly selective private HSs. For example, if a particular HS is selective enough to only admit kids who have a great transcript, top test scores, top LORs, top essays, … then that HS is expected to have a higher rate of acceptances to selective colleges than average. Private HSs usually also much have a higher concentration of ALDC hooked kids than public HSs.
If you only look at the total number of matriculations, without considering number of applications or quality of students; then it can lead to mixing up correlation with causation. I am not saying that the boost is zero for attending a top private HS… more that you need to look at more information than just matriculation totals to draw conclusions. I also expect that the degree of boost or penalty is not constant and instead varies dramatically between different students, including on things like whether they strive in the often more competitive environment of a selective, private HS where a large portion of the class are focusing on attending a particular set of selective, private colleges.
Rather than a direct boost for attending the private HS, I think the bigger advantage is getting a great education, with excellent resources throughout the child’s lifetime. Many non-selective, public HSs offer far fewer opportunities, particularly ones in lower SES areas. And that lack of opportunities and lower quality education often negatively impacts college admission.