While true in theory, is it true in practice? Those with the most resources to mine will mine the most and thus receive the most, allowing them to mine more, and the cycle of centralization continues.
That's true regardless of PoW or PoS, isn't it?
> Those with the most resources to mine will mine the most and thus receive the most, allowing them to mine more, and the cycle of centralization continues.
This is not a problem if the reward distribution is proportional to the investment from miners, which happens when the mining competition has low or inverse economies of scale, and a low barrier to entry.
In PoW and Bitcoin especially, the economies of scale are huge. "Industrial" miners are greatly more profitable than home miners, and ASICs require an upfront investment which comes with risk that smaller operations might not want to take. The result of this high barrier to entry and economies of scale are empirically verifiable by looking at the hash rate from block wins.
A correctly designed PoS system almost completely removes economies of scale (notice I said correctly designed, because many other PoS cryptocurrencies actually explicitly favor larger stakes), but might add some artificial barrier to entry, like Ethereum's 32 ETH minimum. The wealth centralization effect is also amplified in PoS by how directly acquiring the scarce resource required to participate in the competition influences the value of existing stakers' investment.
In Proof of Space consensus protocols (PoST) [1], the scarce resource is storage space. This can have minimal or even inverse economies of scales relative to money invested, as the running costs become almost as minimal as a PoS operation. And since the quality of the storage material is also irrelevant, what matters most is the cost per Tb of acquisition of storage space. The best savings are done on second hand drives, which makes investment in free time rather than money the profit differentiator. The free time to wealth ratio scales inversely, so smaller PoST miners can have a proportional advantage over larger ones. This decentralization effect is empirically verifiable with how much more individual mining nodes the biggest PoST cryptocurrency Chia currently has than Bitcoin and Ethereum, despite the comparatively very low absolute amount of rewards its consensus delivers to its miners.
[1]: full name: Proof of Space and Time, with Time referring to a competition required to get reliable timestamps on the blockchain happening in parallel to the competition over Space.