As I understand it the T14 schools below HYS are all price discounting (under the guise of various named “merit scholarships”) to top profile students to keep their class stats competitive for the rankings. Precisely because there are not , actually, enough high enough scorers to keep their reported stats pumped up to the needed levels without the price discounting. I am actually in contact with a relatively recent beneficiary of this process.
There are of course many attendees from families that are in a position to pay the attendance costs for the kids.
But for the rest, discounting can be effective within the top tier, past the tippy-top of it, because of the huge attendance cost which is not followed necessarily by a guaranteed pay-back anymore. Or certain/ guaranteed differential results depending on the school within the group. If it wasn’t effective, or perceived to be necessary, they wouldn’t still be discounting.