Phase 0 of Ethereum v2 arrives in Q1 2020. Coming since 2014 but finally arriving :)
Proof of stake reduces the issuance of new ETH to pay for the cost of securing the network. It's cheaper than paying miners. And anybody can buy ETH to stake so it's more egalitarian than mining which requires economies of scale in hardware and electricity.
PoS would be more egalitarian if it was that way from the start, however as it is transitioning from PoW this means that anyone that bought in early, now has an opportunity to solidify their position. For new entrants to reach the same level of investment would be significantly higher. So the ETH rich get richer and it widens the gap.
Proof of stake reduces the issuance of new ETH to pay for the cost of securing the network. It's cheaper than paying miners. And anybody can buy ETH to stake so it's more egalitarian than mining which requires economies of scale in hardware and electricity.