Harvard earns enough off trust interest they'd never have to charge another student tuition and room/board if they didn't want to.
They could just take all the smartest kids like this regardless of where they come from.
It's why having the most important part of our education system be for profit has never made sense. Just because you're wealthy or your Daddy went there doesn't mean you should get to take up a spot at one of the best schools on the planet.