I see this story repeated over and and over again on the internet, but I don't really see it playing out the same way in the real world.
I've seen a lot of "rich kids" try to start businesses, but then quickly realize that it's a huge amount of work and not guaranteed success. Then they look around and see all of their opportunities for safe, high-paying jobs that leverage their expensive education and their parents' network, and decide that taking one of those jobs is a much easier way forward.
I lived near a highly ranked MBA school for a while. I would constantly get LinkedIn requests from stereotypical "rich kid" MBA grads who banded together and wanted to "do a startup", but they just needed a few engineers to actually do all the work. It was funny to hear the pitches about how they'd give me 1-5% for doing all of the tech work of their company while all of them (up to 7, in one case) would handle the business side of things for me. No thanks.
There are definitely some "rich kid" startup founders out there, but a lot of the founders I've worked with over the years came more from the end of the spectrum where they grew up learning how to work hard, that money doesn't come easy, that they can't rely on parents to bail them out, and so on.