But does it matter as much for high school?
I totally agree that HYP and maybe Williams/Amherst have a certain, get you in the door name.
I take the “name” doesn’t matter to mean more that if you only apply to the HYP of the boarding school group and don’t get into any you are left with public school but if you apply to a range, some less well known and get into those you will still get a great high school education.