How is this any different than the current situation, where your ability to get block rewards is directly proportional to your ability to spend money on mining hardware?
because anyone can start running hashing computations to generate blocks with PoW (See DMMS)
Proof of Stake requires that you buy the currency in order to create blocks.
If they have the money to buy hashing hardware that's competitive, staking that money has a lower barrier to entry... You don't need space, hardware, or technical experience to assemble the rig. Just $.
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.