You're right. I don't know enough about how legacy/recruited athletes get admitted, so I didn't talk about it. They do, however, get admitted at higher rates, so let me edit that in.

I graduated from Penn a few years ago and have a couple varsity letters. It's similar for athletes, there is just an extra step/another person at the university arguing for you. You still go through the screening process like other applicants and get a ranking, I believe it was called your academic index. The difference is you have some kind of flag on your application that says once you get to the committee, they talk to the coach. Different schools do the flagging differently, not sure how it works now with online applications, but I've seen different colored envelopes, stamps on boxes, numeric codes on sections, or the coach just contacts the admissions office for the heads up. When athletes, like non-athletes, fall into the no pile they tend to stay there, but when you get to a maybe you can have a strong voice for you saying they will add a lot to the community. Each coach gets a limited number of people to argue for and varies depending on sport. One downside to being in the athlete pile is that if you fall in the middle you are very unlikely to get in if you are low on the coaches list. So basically it's another activity with some extra leverage.

Last I knew (= 1990s), Harvard had about 1/3 legacy admits. That number seems incredibly high now, does anyone know a modern number?

FWIW, The rationale back then: Large donors run in families, it was deemed essential to keep the universities funded.

Considering the drops we have been seeing in public funding, at least for public universities keeping funded is perhaps going to become an ever more crucial goal...

Harvard's endowment is $32 billion, equal to the annual budget for the US department of education. I don't think they need to worry.