What are the arguments against proof of stake?

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self.Bitcoin
1/ I don't buy the argument "PoS makes the rich richer", or that it leads into more centralisation. As far as I understand, you get rewarded proportionally to your stake. So, the ratio of wealth remains constant. I will grant that, depending on the cost of staking, it may be a net loss rather than a gain to do it if you have below a certain threshold. 2/ I think there is a lot to the argument that PoS is complex. But that's different to saying it's impossible. Are there any quick intros into the what makes PoS so complex? 3/ With PoW, in theory (not in practice), you can acquire vast computing power, do some double-spends every once in a while. If you manage to destroy the public's faith in BTC, you can sell/reuse your vast computing power. With PoS, you need to buy 51% worth of currency, then effectively destroy what you just bought. So, in a game theoretic sense, it seems safer.