If you think that a very poor person can rise to a Von Neumann calibre genius, then we have no disagreement. I agree with you that having successful parents can only help the situation.
"As for your edit, extreme intelligence is not really correlated to income."
Ok, the marginal correlation breaks down at the extremes. But it's still the case that intelligence and income are correlated, so smarter kids are more likely from higher income parents.
"they'd just need significantly more innate intelligence, which is a very tall order."
I dispute this. Ramanujan is by all accounts on Von Neumann's level and so his example seems to disprove this statement. Or maybe you think Ramanujan has "significantly more innate intelligence" than Von Neumann? It's possible, but without evidence, and a bit farfetched.
I think wealth helps but through a different mechanism to what you're thinking. Avoiding malnutrition is the big one. A secondary point is avoiding the need to work and being able to focus on intellectual passions, which many average-wealth people can do. Adding more money to the picture doesn't help beyond a baseline. Ramanujan was fairly poor but still had enough family wealth to be able to eat enough food and dedicate a lot of time to his passion.
