In current Proof-of-work (PoW) blockchains, the more mining hardware you have, the more coins you get, and the more mining hardware you can buy. In this sense, the same exact monopolistic structure you mention exists in both PoW and Proof-of-stake (PoS) blockchains.

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!