That quote makes a nice soundbyte but I think it has little practical value.
Sorry, my family & friends have conditioned me to keep my Buffett bites short & sweet. But since you asked...
You can do nothing with nothing (or very little). You can do anything with anything - or nothing!
He's publicly mentioned paying for college degrees and buying houses for his kids. His oldest son is on the board (and will probably continue as Chairman) so he's taken care of by the company payroll and whatever shares are handed out to directors. Another son is a performing artist who's mentioned his father's support of his projects. And Buffett even put up with a divorced daughter-in-law writing a book about him.
But all the kids appear to be continuing to work by choice at least as much as by budget. I'm not sure about the subsequent generation(s), but I'm pretty confident that they won't be cluttering up the Forbes 400 list like the Walton heirs.
I know many people who could retire but keep working because they enjoy what they do or the challenge.
And more power to them-- if they've found their avocation then they'll never have to work again! But it's awfully hard to distinguish avocations vs jobs among those who claim to have found their bliss while they're actually working to be able to pay their bills.
I know a retired flag officer who's nearly 80 years old and receiving what has to be at least six-figure federal pension with a COLA. He claims that he's enjoying himself too much to quit but his spouse pulled mine aside and asked how we managed to retire. My spouse started talking about savings, mutual funds, ETFs, stocks, and owning our house. His spouse said "Oh, we never had any of that." My spouse asked "What, stocks?" and she replied "No, savings"...
I think it comes down to a person's character and work ethic, and how they were raised, not how much money they may have been left.
We all know posters on this board, ER'd or close to it, whose siblings or parents have nowhere near the skills, knowledge, or intent to be able to ER.
I think that a person's character & work ethic will develop until the development is halted by affluenza. That seems to happen to some kids as teenagers while others manage to make it to adulthood and do just fine. I suspect it's a function of how much of other people's money you can get your hands on.
Look at the biggest expenses that a young family w/ kids faces: private school tuition, college tuition, extra education and enrichment opportunities, an expensive house (if you want to live in a nice/safe area), health care (dental, orthodontics), etc. I always saw family wealth as a way to help provide these things for the youngest generation. Maybe that is because I was raised around a lot of immigrant families whose attitudes seem to differ from the traditional blue collar American attitudes.
I think it's a parent's obligation to give the kids the tools they need to succeed after high school. For some parents it's a hammer & screwdriver, for other parents it's an entire NASCAR mechanic's trailer. And some parents will even build the kid's house, fill it with furniture, and provide 24/7 room service.
I think that parents should provide the basics of housing, food, clothing, education, and a safe/loving environment. But by the time they're teenagers you'll be able to figure out whether it's worth paying for their college education or suggesting that they apply to a nice military academy. Any support beyond high school has to be weighed against the consideration that it could very well delay the parent's own retirement.