Unless by rich people you mean lottery winners and Instagram influencers, the truly rich people have top financial education, trust funds and top wealth management companies that keep their wealth growing so they can't make mistakes.
If you look at any list of the truly rich, it is almost all 'new money', of those that are beneficiaries, the money was inherited relatively recently (such as the Walton family).
There are a bunch of other things to consider, for instance diversification of wealth has fundamentally transformed since the early 1900's and wealth management is on a completely different level than even 20 years ago, let alone 120 years ago. Not to mention the legal innovation to protect estate value that has been going on.
I'll also point out that the people on that list are generally not using Fidelity, Vanguard, or Hancock as their wealth management services. They are using private family offices or firms like PDT Partners that are directly accountable to those families.