I have heard that it began to try to keep certain ethnic groups out of university and continued because sports bring in scholarship and (for D1 schools) sponsor money.
Not just ethnic groups. Schools mostly can't say "we only want rich people" but they definitely want to prefer students who will contribute to the donation revenue stream either themselves or through their parents. Signals like "doesn't have a job to take up their time in high school" and "parents can afford (and have the free time to enable) expensive, time-consuming activities" are really good proxies for that.
Yes, absolutely. The kids who can assemble a resume of primo extra-ciriculars and volunteer experience are the ones from wealthy and well-connected families. Even the kids who can write the best essays about their troubled upbringings are the ones with access to lots of coaching lol. If they just have to be smart and show up for their government mandated 7 hours of classes, the poor kids can keep up. They can't keep up with another 5 hours of homework and resume-sweeteners every day.
I knew someone who got into a good school on a crew (rowing) scholarship. I remember thinking "wait doesn't almost everyone who rows crew go to a wealthy private school?"