I am skeptical of the argument that proof-of-stake will decentralize ownership. The argument in favour of it is that POS has lower capital requirements, so easier entry to the market. That makes sense, but I think it is naive.
Suppose person A has 1,000ETH and persons B, C, D, ... have 1 ETH each. Under POS, if everyone participates in the mining, they will maintain these ratios.
Under POW, the new coins are allocated to participants in proportion to their hashpower. If person A has only 10x the hashpower of persons B, C, D ... then over time person A will have a shrinking proportion of the coins. I argue that this is the realistic scenario, for the following reason.
The richer you are, the greater opportunity you have to diversify -- to invest your capital elsewhere (person A will probably not buy 1000x the hashpower of the other players) -- creating market opportunities for smaller competition in the vacuum they leave behind. Under POS, the rich remain rich and the poor remain poor. (Also, persons B, C, D, ... being poorer, need to spend a greater proportion of their capital, rather than invest it.)
In other words, POS strikes me as being regressive.
Am I right, or is there an argument that, taking the above into account, POS will decentralize ETH holdings?