This is generally true. The Vanderbilts, Astors, Morgan, are all gone. There are exceptions shielded by ingenious investments and trusts. But even those become diluted by beneficiaries over time. For instance, the Rothchilds may be worth well over a trillion, but there are tons of them.
There are two viable paths to deal with an entrenched monster. They must either be slain or caged forever. I don't see Lydia or Finn being up for slaying, so an effective cage it is.