Wouldn't ETH (or any coin) with proof of stake make it a 'rich-get-richer' scheme?

As it is right now ETH has imo a bit of a 'rich-get-richer' issue with proof of work being dependant on hardware which you have to buy.

ETH switching to Proof of stake would give it a similar issue where owning more ETH means you get more ETH, right? Has anyone else thought this might be an issue later on where a small percentage of people owns (and will keep owning) the largest sum of ETH? If so, what would you say might fix this problem, and if you don't see it as a problem, why not?