This!! Highly selective schools are not looking for more boarding school kids so it’s not an advantage. But others are (SMU, I’m looking at you!). SMU, in its bid to have a more national presence, is affirmatively targeting BS kids because SMU believes it will raise the school’s profile in the Northeast. I think they are right. One or 2 kids from my son’s school went every few years, but my son’s year 5 went from Hotchkiss. And the next year SMU started rejecting some kids.
My other son got merit aid from his match and safety schools (about $10,000/year for matches and about $25,000/year from the safeties). And he didn’t have a world beating GPA.