The problem is that when people get unearned money they usually become wasteful and lose their drive. It's also really hard to keep working on something financial when you've got a large external income; if you're making a million bucks a year in investment income then spending all your waking hours on a business that's making fifty grand a year doesn't seem worthwhile even if it might eventually grow much larger.
But I'm guessing the children of successful business people also get, besides the money, a great education on business. More importantly, they probably inherit a great worldview of money/business, which drives them to also try and do great things.
This isn't true in every case, but it's probably true in some cases. I'm guessing any child of a person like Bill Gates might be given the kind of education which pushes him/her to great heights. Should probably check some statistics on this issue.
Even though people are rich doesn't mean they are smart. Survivorship bias