I think you are reflecting on survivor bias for successful people.

Almost all rich families I met saw entrepreneurship as lower-status. They chase arts and such. They are posturing they don't need to care about money. [of course it's a lie, but they do it anyway]

Only a fraction of the new rich get their kids into entrepreneurship while the rest are just spoiled. I heard many times "I want my kids to have all the things I din't have growing up" and then the kids turn into horrible entitled brats who hate their parents. Then the inevitable "How could they do this to me! I gave them everything!". It's not easy raising kids, even with enough money.

What's the solution to that problem

Nothing can be done about that.

We need to focus on ways to boost class mobility at a young age.