Okay, I promise to stop! But… Just one more post…
These highly selective BS maintain their reputations, not just with applicants but also with the colleges where they place them, by doing the best possible job of preparing their students so they will be compelling applicants. If asking them to repeat, or even accepting repeats, undermined that goal, it seems unlikely they’d persist in that practice.
Perhaps in a different tier of private schools it would be frowned upon (if it happens there, which @fretfulmother has indicated it does), but it doesn’t seem to be a problem for this group of boarding schools. Could be, as @ChoatieMom points out, we’re talking about 2 different things here.
BS requires a certain level of independence and maturity which a kid, regardless of academic prowess, may lack, and this no doubt plays into that decision of whether to admit them a year later. Colleges are then looking at the whole package, not just how far along in a math progression a kid is or how fast he’s done it.
Fwiw, there are a number of BS who don’t have many repeats - really depends on the school as well.