Again, you're trying to take the Gilded Age as a prime example, when there's already evidence that shows it's not going to be that way.
Gates and Zuckerberg are, to my understanding, giving away only tiny fractions of their wealth to charity. A far cry from Carnegie.
Their foundations remain powerful engines for them, and their heirs, to control the money and how it gets spent.
And the norms have changed since the Gilded Age: at that time, there was still a very strong culture of honor, dignity, and genuine service even among what were then the "nouveau riche" that is utterly absent today. Indeed, one of the primary hallmarks of today's right-wing movement is the aggressive denial that dignity and respect are things that should even exist. (Except, of course, for them.)
For children raised in that kind of environment, the very best we can realistically expect is that they will simply squander the wealth and have little direct impact on the political sphere.
Here's hoping that after 100 years, the only thing that lasts about this crop of robber barons is their names as a cautionary tale in history, about what happens to the wealthy when they forget that they are few, and we are many.