I suspect one of the big advantages that money brings to the kids of the rich is to have not only one-on-one education, but also the best-of-the-best in each subject.
That said:
> classical studies
While this may be the "cornerstone of an elite higher education" as Wikipedia calls it, IMO (like studying Shakespeare[0]) I'm not convinced it is a productive use of time.
Don't get me wrong, nerd out about anything you like, but a lot of the world shifted since then. The overlap between what you learn from studying people who thought the sun was a chariot drawn over the sky by magic horses and that the Sahara was caused by some idiot driving them wrong, and what you need to know to deal with a highly connected globally integrated supply chain, is not exactly zero; but childhood is limited and you are likely better off focusing on what's actually in the modern world.
That said, of the few ways it is still useful is likely as shibboleth for the powerful to know one another.
[0] Shakespeare's closer to us than the ancient Greeks and Romans, of course, but still a very different world, the plot of e.g. Merchant of Venice just can't happen today. Plus he was seen as merely "good" rather than "the best"[1] within his own life, was clearly reworking other older tales for his audience[2], his plays were his era's version of somewhere between MCU, a soap opera, and stand up: the goal was bums on seats not high art, it was watched by a broad audience including normal people not just the era's version of evening-wear, crowd participation was a thing, actors would need to be reminded their lines in the middle, etc.
[1] https://en.wikipedia.org/wiki/Reputation_of_William_Shakespe...
[2] e.g. https://en.wikipedia.org/wiki/Sources_of_Hamlet, https://en.wikipedia.org/wiki/Amleth, why yes I do only know about Amleth from SMBC