Elites have access to social connections that most ordinary people don't -- both in quality and quantity. This is the most defining advantage that they possess over the public, albeit money and name recognition don't hurt either.
[1] https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2473238
And this is why elite schools are worth it for the elite. You may or may not get a better education there, but you meet better contacts there. (You make contacts at a state school too, but the contacts you make are people who went to a state school, not people who went to an elite university.)
Also, knowledge about how to run organizations.
The real skills gap is between the, I don't know, maybe ninety percent of us who work in office jobs and could be easily replaced, compared to the maybe ten percent who have really invested in learning their trades (whether it be rocket science or plumbing) and cannot be easily replaced. My generation (GenX) was taught when we were kids that we should be "knowledge workers" and get paid a lot for doing very little. The end result is, most of us are in jobs where if we quit tomorrow, the boss could have a replacement hired in a month. We were pushed to be "generalists" with the idea that we could have a whole bunch of different careers, rather than spending our lives doing one thing. But the joke's on us: those people who spend their lives doing just one thing are the ones most valuable to the world.
Middle-class acquaintances all went directly into something that pays the bills: trades, engineering, law, etc. They know how to do things, but not what to do. They all work for the man.