Several articles in the last month or two have mentioned "wealthy" private schools, including eye-catching tables and charts. Possibly this is intended to invoke "shock horror" or "omigod, how they can be so wealthy and still charge fees (or such high fees". Other than coverage of US college endowments, in none of these pieces have I seen a breakdown of what comprises this wealth, and even in the case of the endowments, a simple number without explanation or context probably provides a false picture.
My suspicion is that the majority or even the entirety of a school's wealth lies in its property, buildings and facilities. A homeowner with a $400.000 hours and $0 in the bank has wealth of $400.000, but s/he still has $0 in the bank. Similarly, a school with a value of $100 million may have land, buildings and sports facilities worth $100 million and is running on cashflow from tuition payment.
If the homeowner were to sell his/her home, she would now have less wealth but would still need somewhere to live and so may simply replace one $400.000 house with another or become a renter. In any scenario, s/he is still not really wealthy since a home is still required and may well be later sold to fund elder care.
However unlike a homeowner, a school cannot move to a cheaper area or downsize. A school exists in its community and schools tread very carefully when considering re-locating, I know of several non-public schools which moved from an older established neighborhood to the edge of town so as to have more space and they lost most or all of their old families and student body and so became a different entity.
Similarly, a school cannot easily downsize its sports facilities or library or science block. Again, I know of several non-public (and public) schools which sold sports fields because they needed the cash with the inevitable result of a diminished sports program and in many cases, no sports program at all.
And of course while non-public schools own their land and buildings, in the case of public schools ownership rests with the district or local or state government making any comparison of "wealth" inaccurate.
Endowments are also tricky things as often they are conditional. For example, the school "owns" the endowment while it continues to do whatever is specified, eg run an equestrian programme, but as soon that is no longer done or varies too much, the school loses the endowment. Often, the school merely holds the endowment but only has access to income therefrom and has no access to the principal funds; schools have closed due to a lack of funds while also having an endowment.
Some private schools may indeed be wealthy, but without a breakdown any such claim is misleading at best and any comparison with public schools is probably just wrong.
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