The exact same way proof of purchase of massive bespoke mining rigs doesn't cause the rich to grow richer.
The people making significant money from mining cryptocurrencies are the ones with multiple warehouse-scale operations filled with custom hardware. These people aren't getting rich, they were already rich. Moving to PoS just removes some middlemen, not changes the fundamental economics.
Real estate is a pyramid scheme. So are stocks. And even money itself. Anything of value is ultimately hoarded and concentrated in the hands of a few. It's not an issue unique to crypto.
Even beyond that, a PoS system is still, like all cryptocurrencies, functionally, a pyramid scheme.