Why would we care about "advantage within the protocol" while ignoring the whole world around it? A similar absurd description is: one person is holding $1B in their hands, another is holding $1 - neither has more say about the money nor any advantage within the system as long as they don't spend it. It's true, but not very meaningful - we do things with money we own.
Bitcoin's premise is scarcity and software-enforced rules that are equal to all. It isn't going to "fairly" distribute existing capital, that should go without saying.
I think the problem with PoS is not "rich get richer" but the lack of fair redestribution. In PoW miners are economically forced to sell their mined coins to pay for energy bills. This redistribution is fair as it happens on the free market (exchanges). This doesn't really happen in PoS.
Whereas staking is more like bringing fiat to the bank and collecting interest for doing nothing at all.
Still, you do have a point in the sense that if you're as wealthy as having 1,000 BTC, you have ample ways to further grow wealth. You could sell all BTC, go into real estate, take profit and buy back BTC cheaper. There's a million ways to grow your portfolio.
It's just that Bitcoin doesn't give you more Bitcoin based on wealth. Most Bitcoin held is not held by miners.
There seems to be this narrative where some people believe miners are minting and then holding all the coins, getting ever richer, but this is plain false.
It would be true with PoS though, so agree.
Rather, we should look at holders. Bitcoin is fair in the sense that it does not have rich get richer built in.
If I'm rich and own 1,000 BTC whilst some poor slum has 0.001 BTC, neither of us has an advantage within the protocol. The rich person does not get free extra coins just for owning lots, nor do they have any additional say anywhere within the protocol.
With PoS, just having lots of money means you get free new money, as well as an extra say in the protocol itself.
Further, you should speak of electricity consumption combined with the energy mix. Electricity consumption does not automatically translate into pollution.