Their wealth is scarce in that they can't share it endlessly. No one is ultra-wealthy enough to say, "I'm going to give $1 million to random people so that people don't have to suffer anymore. That's a critical difference.
Plus, of course the physical limitation that no one can ever be rich enough to share endlessly.
Then the super-rich will start sharing their wealth, because if they don't, their competitors will do it first and take all the fame. It is not from the benevolence of the super-rich, the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest.
I don't think I'll be holding my breath waiting for ultra rich to be motivated by fame of this type. In fact, I think it's wishful thinking in its finest form.