It can be applied to any hegemonic class, really.
But yes, it’s rich people. Public schools may have originally risen out of defiance of the hegemony, at least in some notably locations, but they were quickly captured by it.
Schools over a place where the rich of the past can be aggrandised, and the rich of the present can ensure the workforce gains the basic skills to keep making them money, while also hearing about how it is right, and natural, and inevitable that they get to keep the product of your labour.
“I’ll tell you how I feel about school, Jerry: It’s a waste of time. Bunch of people runnin’ around bumpin’ into each other, got a guy up front says, ‘Two plus two,’ and the people in the back say, ‘Four.’ Then the bell rings and they give you a carton of milk and a piece of paper that says you can go take a dump or somethin’. I mean, it’s not a place for smart people, Jerry. I know that’s not a popular opinion, but that’s my two cents on the issue.” — Rick