It's counterintuitive but PoS is fairer than PoW (as we know it).
Economies of scale: a proportionate saving in costs gained by an increased level of production.
http://www.investopedia.com/terms/e/economiesofscale.asp
PoW miners have to invest their capital in hardware. The costs of running a mine is composed of fixed costs and variable costs.
Fixed costs: Renting space. Internet access. Administrator 24h on duty Variable costs: power consumption, mining hardware
If you are a kid mining in the basement of your parents you might not have many fixed costs, but you can't even scale or the electricity bill will get you in trouble.
If you have a serious mining farm on the other hand, you have a certain capacity in your mining plant where an additional hashpower will not increase your fixed costs. You even can optimize everything to a high level of efficency.
Economies of scale means the rich have an marginal advantage over the poor, PoW has economics of scale
Wikipedia - economies of scale: costs per piece are reduced by more output
With PoS fixed costs are negligible: no space to rent, no admin to hire.
With PoS the marginal advantage of the rich over the poor is zero
PoS is not perfect but, it reduces inequality and improves security by incentivizing small stakers to contribute.