For reference, Cornelius Vanderbilt was the wealthiest man in the US in the late 1800s. His income alone made up a significant percentage of the total GDP of the entire US.

Nowadays, the wealthiest descendants are probably Anderson Cooper, and the family members who own the Biltmore estate which, at one time, was primarily funded by a successful dairy farm ran on the property. One is also a relatively successful movie producer, as well.

I'm sure that none of the heirs are destitute, but none of them are building 50,000 square foot mansions in Malibu, either.