If someone who's rich wants to spend their time becoming a doctor and has a genuine interest to help the world, more power to 'em.
They obviously aren't doing it for the money. They could sit around and do nothing all day, other than manage their money. Sure it's a little annoying to the people trying to get in, but I don't think the schools are accepting UNQUALIFIED candidates, but rather people who already might get in but have this family name or whatever to help them.
What's far more frustrating to me is that level of wealth right below filthy-rich: the kind where parents hire people to do their children's homework and write their application essays, etc. etc. It's not common, sure, but I find it far more disturbing than a family that donates money to a school and gains some benefit from it.
Also note that one of the parents is usually an alumnus or alumna of the institution. In this case, their kid trying to get into medical school already has the legacy advantage anyway.
In any case, I guess I'm just desensitized to this concept by now. It's the same reason you'll see the son/daughter of every president at a top-flight private school and the same with prominent businessmen, literary figures, etc. The kids might have merit, but I feel they don't have to do as much to prove it.
And from the school's point of view, it's an issue of pride. And networking. The students who go to Harvard rub shoulders with the kids of a lot of important people. You're bound to become friends with some of them and probably meet their parents at some point. One of my friends who goes there was flown out to the Hamptons for a party at a mansion, and subsequently was given a job offer (he's in business) from his friend's father. No doubt in my mind that this is one of the biggest draws of attending a school like the Ivy Leagues or Stanford, etc.