Distribution of hashing power requires capital investment and so tends to centralize. Capital investments to issue proof of stake coins that keep wealth re-distributed are negligible. But please read the next paragraph.

Imagine you live in a small community in the future in a failed state like Venezuela or hyperinflationary environment and fiat currency loses 10% of purchasing power every week. This small community can delegate a local authority to issue a proof of stake currency to service the local economy. Since the number of coins in circulation is known, the local authority can't easily abuse their power issuing more currency than necessary for fear of being thrown out of the office by an angry mob, but this is not the only difference to government moneys. People are not required by law to use this community scrip, remember that fiat is "money by emperor's decree". There is no reason a plumber should want to make miners in China and early adopters rich buying Bitcoin if all he needs to do is keep accounting with a local grocery store. The plumber may save his excess earnings in something else he considers more stable than local scrip if such a thing exists. My point is there will not be one as it's more convenient to use locally issued proof of stake credits to service small local economies, keeping wealth in the local communities because there is no top-down money production scheme imposed on them, whether it be government fiat or chinese Bitcoin miners.