Proof-of-stake requires the majority of what is mined has to be sold on the open market. This redistributes mined coin to any user anywhere, rich or poor. If you mine and do not sell, you perpetually consume and fail in short order.
Proof-of-stake doesn't require this natural, market-driven redistribution. It exchanges it for an inflationary process that further separates the rich and the poor.
You are completely ignoring second-order effects for these systems. You can quite easily turn resources obtained from a PoW system into a PoS financial system and have the worst of both worlds.
Do you want an example?
> If you mine and do not sell, you perpetually consume and fail in short order.
With ETH you can mine ETH, lock in a MakerDAO vault and pay your operations with very low-interest DAI and use that to finance all your operational costs.
As long as your profit from mining is higher than the interest from minting DAI (which is very easy to do), you can mine forever without ever giving up the original ETH. Your only limitation would be in how many people would be willing to buy all the DAI you will be minting.
This is no different than a PoS system, except that it still has to bear all the PoW costs and externalities.
> they're just not the point being discussed here.
In other words, you are ignoring (not paying attention, leaving aside) an aspect that should be considered.
(You asked for a good-faith conversation, but after these types of replies it gets hard to take you seriously. The quote "It is hard to get a man to understand something when his salary depends on not understanding it" becomes more and more apt with each response you give.)
Read again. I described an mechanism that you can be a miner of a PoW mechanism and still be able to finance your operation without selling the asset you mined, effectively turning the economic model of it from PoW into PoS, while keeping the horrible externalities and costs of PoW.
Proof-of-stake doesn't require this natural, market-driven redistribution. It exchanges it for an inflationary process that further separates the rich and the poor.
They're fundamentally different.