As an example, the proposed proof of stake mechanism for Ethereum requires 32 ETH, which is around $100k USD today. So established parties with capital will be able to stake, but your average person will not. I'm not sure I like that aspect of it.
Consider the case with Proof of Work (ASIC-based): you need to purchase specialized hardware for several $k (apparently at least $2k), spend more on specialized infrastructure (power supply, cooling, servers) and live somewhere with almost free energy. Otherwise it's just not economical to mine. This leaves out the vast majority of people as well, and incentivizes (1) massive economies of scale of farms, (2) shady or corrupt deals for free energy, through local government or simply illegal connections to the network.