However, (PoS) is a lot less monopolistic than PoW for other reasons:
1. Massively reduced economies of scale. Pretty much all POW mining happens in mining farms for a reason: it's a lot cheaper, per unit of revenue, to move all your mining to one big warehouse. This makes it pretty much impossible for a normal person to contribute to PoW in any meaningful way -- good luck running a competitive mining farm out of your house. In PoS, however, 10x more coins will get you exactly 10x more rewards, and costs don't fall at all, leading to less economies of scale, and so less pressure towards a monopoly.
2. Ability for the protocol to apply punishments as well as rewards. In PoW, because the miners aren't tied to any address, there is no real mechanism for punishing them. In PoS, because the "mining power" (aka coins) is in the protocol, bad behavior can be punished. This has two benefits from the perspective of monopolistic market structure. First, it makes it so 51% attacks are costly in protocol. If evidence is shown that you 51% attacked, your coins can be "slashed," or taken away. Notably, in PoW, a 51% attack is free to the attacker if successful. Second, collective punishments can be applied to miners (validators in PoS language). This makes it so miners can be punished if they censor other miners -- again leading to less centralization/monopoly pressure.
Please do disagree (or make me clarify) with anything that seems stupid/unclear/incorrect in the above. I'd love to engage more!
Where do the coins come from? Has there been any other mechanisms for minting other than minting the supply from day 1, or burning computational capital/energy in the form of PoW mining?
In most PoS protocols, coins come from either PoW mining before a transition to PoS, or from an initial coin offering. Neither are great solutions IMO, but PoW doesn't really distribute coins very well either.
In terms of implementing PoS, most BFT algos have traditionally scaled poorly (HotStuff which is linear in communication costs relative to the number of nodes/validators is very recent). In addition, going offline for validators, even accidentally, hurts the network and slashing PoS schemes often have uptime requirements. Validators also need to have the infra to be hidden and not DDOS'd.
tl;dr, Proof of stake is still decently centralized, but a lot of work is being done to scale it.
Also, w.r.t. linear communication, CBC Casper[2] has the ability to come to consensus on a blockchain with, in the limit (and in the optimal case), a single message per block that is finalized. It uses essentially the same form of pipelining that HotStuff does, but to the extreme (at at the cost of a much longer time for blocks to be finalized). Full disclosure: I work on CBC Casper, so take what I'm saying with a grain of salt.
[1] https://dahliamalkhi.wordpress.com/2019/04/24/flexible-byzan...
[2] https://github.com/cbc-casper/cbc-casper-paper/blob/master/c...
The 1/3 bound is without any synchronicity assumptions; with strong synchronicity assumptions you can get to 1/2. This seems strictly better than PoW (no liveness at all in an asynchronous network, and 1/2 with synchronicity assumptions).
PoS - you can just buy your way in, and stay in. Great for whales.
Whales should be kept at the currency value layer, not in the network layer, because whales are greedy and dangerous.
To respond to (1) I think I don't understand the mechanism of proof-of-stake well enough. I think (correct me if I'm wrong) that the reason pooling is incentivized in proof-of-work is because having more mining power doesn't give you more coins as much as it increases the likelihood of you receiving a coin. In other words, it's the statistical nature of proof-of-work that makes pooling necessary. For proof-of-stake to not incentivize pooling I think it would need to not distribute coins statistically, but more like how stock dividends are issued today.
That being said I'm still not sure that the incentive for miners to pool is the same as a pressure on the network to consolidate holdings. I'll need to reflect on that.
Regarding (2) I'm not sure I understand why or how you would punish participants. ie. how would the network differentiate a 51% attack from a "legitimate" use of 51% to steer the network, and what could it do as a result?