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Now that that is out of the way, I don't necessarily believe that Argument 1 is inherently true (I know you aren't necessarily supporting it but I figured I'd throw my 2p in).
Ultimately Proof of Stake is just moving from a system with an external resource to one with an internal resource. This theoretically allows you to largely divorce the system from the harsh realities of the outside world (whose rules those external resources are bound to). By isolating the system you can better structure the rules of the game (from a game theory perspective) without being influenced or bound to rules from the outside system. Of course this isolation is only as strong as the network (larger market cap makes attacks harder) but generally once the network reaches scale it is largely independent of the outside world.
How a system influences the distribution of wealth ultimately depends on those rules in the system and by PoS largely granting the system the ability to decide those rules for itself, you can theoretically design a system with an expected steady state at or around the middle class at which the system can help lift those with less wealth up and weigh those with more wealth down. Balance it incorrectly and you run into issues one way (concentration of wealth) or another (lack of staking support opening up risks for attack) but theoretically it can be done right.
One of the key features of that balance is that wealth is worth the same whether it is held by many people or one person. It should be just as viable for a thousand people to lend 100 dollars as it is for a firm or wealthy individual to lend 100k with both groups exposed to the same amount of risk all other things the same.
Various mechanisms of the network including staking (including delegation), access to a democratically controlled treasury, first class support for governance primitives, and other such features are essential for making such a system work. Proof of Stake on its own may generally provide an accrual of wealth but in combination with the other forces on the network it should be perfectly viable to create a network that promotes distribution towards a reasonable steady state (with deviations due to merit of the individuals or just outright luck and not maintaining such deviations long term).
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/rant
I'm generally pretty cynical but no matter how hard I dig into it, I can't find a reason why PoS shouldn't be one of the last pieces of the puzzle to produce such a system and if it's even just a chance I think it's exceptionally valuable that we pursue it. Or maybe I'm just a crazy Crypto-LibSoc. ¯\_(ツ)_/¯
