With the current trends of prices in crypto and the long term vision supported by the community (HODL!), the implementation of Proof of Stake could eventually derive in big ETH stakeholders getting the majority of the mining fees. Will not this derive in a more fat-tailed distribution of the currency holders, continually increasing the wealth inequality of the system?
At some point you're right, as ETH stakeholders will more likely be chosen to mine the next block of the chain, the risk you describe exists.
However this is a problem that already exists also with PoW. If we take bitcoin, a small minority of miners represents a big majority of the hashpower. Why ? Simply because to be able to compete with the biggest mine farms you need to deploy an infrastructure you'll need to inject a lot of money to build it.
Also, something to consider is that maybe there is not perfect consensus, and different consensus should be deployed depending on the state and maturation of a blockchain.
PoW bring it's bunch of limits, as PoS & dPoS seems to bring its own bunch of limits, etc.
Consensus debates are a deep subject, we could consider at a still experimentation maturation, but that makes it nonetheless fascinating.
i'll leave you here a topic of reddit where this topic has been debated but pretty sure you'll find tons more on many places ( blogs, bitcointalk,etc. )
Ethereum has a naturally disequal wealth system, given the nature of its ICO. With the proposed PoS protocol, only those holding at least 1200 ether will even be able to stake -- you're right, the rich get richer. See this answer - "Ethereum was never meant to be used as a public currency" - What are the impacts of the Ethereum pre-sale, pyramidal wealth distribution, and mysterious lack of concern within a decentralized financial system?
I hate when answers reply to questions like these with "Whataboutism" (What about bitcoin? What about the dollar? etc). The only legitimately proposed crypto movement that I've seen that takes this equal-wealth-distribution concept to heart is Project Oblio. It is an ICO-less project working with a fork of geth and brainwaves to anonymously identify users in a dPOS system, while creating value in the form of brain-boosting and depression treatments. It's the first immediately useful crypto that I've seen, and whoever its founder is seems to "get it"... Will people really want to join an "old boy's club" of wealth as many ICOs have set themselves up to be, etc.
Note: I do not work for Project Oblio nor am I invested in it (as far as I can tell, it hasn't even released a coin yet), it is just a project that I am following.