If you're among the 1-percenters' offspring whose parents either went to these elite institutions or can afford to donate something substantial to get you in, why is it surprising that elite schools have more well-off students? There will always be efforts by the institutions in the form of scholarships and flexible admissions practices to diversify the student body, but the top colleges are definitely a pay-to-play operation.
There's basically 4 factors that determine where you end up in life -- how smart or successful your parents are, how wealthy they are, how much raw potential you have, and usually a whole lot of dumb luck. Smart or successful parents can afford to live in a good school district and provide a stable environment for their kids. Really rich parents can buy their way into the elite prep school track. Really smart students can often succeed enough to overcome a bad environment. Anyone can get lucky and just have things sort of work out for them. In my case, it was a combination of a good home life and a lot of right place/right time luck. I wasn't a good enough student to be in the scholarship bucket, and my parents weren't rich, but I did go to a decent K-12 school system and had involved parents who kicked my butt enough to do reasonably well. My dumb luck was getting a part time job doing tech support for the state university I went to, eventually doing it just short of full time, and using that to get my foot in the door at my first IT job.
The reason the elite schools will always have the lock on the 1% crowd is that once you're in, regardless of how you got there, you don't have to rely on luck. It starts with non-religious elite private schools. If your family can afford college level tuition for a K-12 education, there's a tacit agreement that one of the elite universities will have a spot for you. (Seriously, one school near us charges almost $40K for grade school tuition, but it's in the top 15 or so among elite boarding schools.) If you can get into and graduate from a Harvard, Yale, Princeton or similar, the school and its alumni network will not let you fail. White-shoe management consulting firms exclusively hire from the elite universities, and that's probably one of the most lucrative jobs a new graduate can have. The same goes for investment banking -- going from being a broke college student to making $250K a year is a big change. People who work for investment banks, management consulting firms and other similar employees mysteriously tend to wind up in very lucrative positions at their clients eventually, and the old boys'/old girls' network perpetuates.
This is why I feel states need to invest in public universities. It's basically the only lever the non-elite among us have to get ourselves to a better situation. If you're not smart enough or have a unique enough situation to get a full scholarship to a private university, your best bet in most states is to go to a big public college and milk your time there for all it's worth. I'm socking away money for my kids' college education, but unless they turn out to be absolute geniuses this is going to be the advice I give them too. Life may be a matter of who you know or dumb luck sometimes, but it never hurts to increase your chances. If you work hard and have a good run of luck, it is still possible to at least be comfortable. We'll see what the future holds though.