Rich people in a proof-of-stake system will stake their money because doing so gets them more free money for no cost. Rich people in a proof-of-work system have to choose between spending their money on hashing hardware and spending it on other things.
The thing about rich people is that they don't spend most of their money. Instead, they keep it locked up in relatively illiquid investments that yield big returns over long terms. The poor are stuck with riskier short term investments, if they can afford to invest at all.
