That's simply not true. The cost of the bitcoin miner itself is insubstantial (a small percentage of its total lifetime cost), the primary cost of mining is the commodity energy cost.
If you had a lot of capital, you could also deploy that capital completely outside of crypto, multiply it, then come back into crypto to have a larger stake in the crypto assset than you started. So your comment is true, but really applies to every freely traded economic asset.
Anyway, the mining/staking in crypto isn't primarily about increasing wealth, it is about defending the blockchain. In this aspect, there is a huge difference between the PoW and PoS. If someone has >50% of a PoS token, there is no way to usurp their control of the blockchain unless they willingly sell their tokens. With PoW, because the mining uses a different resource (energy), it is always possible to invest more capital to usurp the control of the blockchain by creating a larger hashrate. The ownership structure of the actual PoW token doesn't really matter, because outside capital can be introduced into the system.
Why would it converge when we are already starting with concentration? PoS would only work if we all started with nothing from t=0 which NO ONE in the crypto space would concede to because they don’t want to give up their wealth. So in the end, you end up with something even worse than current state of capitalism.
I'm just saying that 'staking' in proof of stake isn't materially different than taking your Bitcoin and purchasing a share of a company that mines Bitcoin. [edit] you can always un-stake by selling your share.
Staking is similar to buying lottery tickets at the store, except you need never leave your home or pay any money for the tickets. It’s all about passive income generation.
Mining is a business, with real costs and logistics to fret about.
People should really stop doing the mental gymnastics to make push-button passive income generation seem extraordinarily challenging and, even more egregious, extremely equitable (“it’s _at least_ as fair as Bitcoin”).
Conflating the two things like this is completely ignorant.
Buying Bitcoin miners at first requires you to spend the Bitcoin.
Mining may help you gain Bitcoin, but it doesn't much allow you to control Bitcoin.
Pos literally gives you voting power over the currency's ecosystem just by having more of it. It completely concentrates control, and then it also returns gains to those with the larger stake (more wealth in said currency).
If you have significant fiat capital you can easily purchase mining power in PoW. Similar with purchasing validator power in PoS. The two are equal in that regard. Where they differ is that PoS is more resilient to 51% attacks of this nature than PoW is.