(A dry postscript on those who say that feckless descendants correct this problem on their own: "It would in any case be rather imprudent to rely solely on the eternal but arbitrary force of family degeneration to limit the future proliferation of billionaires.")
That also creates unwise incentives for the grifter class who prey on the indolent douchebags of the later generations.
As ever, Vonnegut cut to the heart of it:
"It's still possible for an American to make a fortune on his own." said his father.
"Sure--provided somebody tells him when he's young enough that there is a Money River, that there's nothing fair about it, that he had damn well forget about hard work and the merit system and honesty and all that crap, and get to where the river is. 'Go where the rich and the powerful are,' I'd tell him, 'and learn their ways. They can be flattered and they can be scared. Please them enormously or scare them enormously, and one moonless night they will put their fingers to their lips, warning you not to make a sound. And they will lead you through the dark to the widest, deepest river of wealth ever known to man. You'll be shown your place on the riverbank, and handed a bucket all your own. Slurp as much as you want, but try to keep the racket of your slurping down. A poor man might hear.'"