Why proof of stake has no value:
Since Satoshi did not solve the Byzantine generals problem, this means confirmations are completely arbitrary. So why are two confirmations more useful in Bitcoin (PoW) than one? Because it's an open entropy system where over a period of time, it's either unlikely or statistically impossible for someone to maintain a monopoly on block validation when there's no upper limit to confirmations.
Recursive systems like proof of stake tend to permanently monopolize block validation by design, with no real fault or state recovery to fix it once it goes off the rails. The act of introducing interest compounds this problem even more. This makes a proof of stake confirmation essentially worthless due to being a bounded entropy system.
On top of being worthless, proof of stake is also a permissioned ledger. The purpose of mining in Bitcoin is to create a permanent decentralized exchange peg, which thus results in a permissionless system.
Ok. Let me explain, why this is wrong with this example:
POSOne has bought 1% of the coins and getting therefore 1% of new coins and transaction fees. His stake is growing in percentage to other (smaller) accounts, if he doesn't spend any coins.
You say he is getting richer all the time and POW is different?
POWOne has bought 1% of hashing power and getting 1% of new coins + the transaction fees.
If the miner uses the whole money to buy hashing power. Guess how much much his % grows compared to the other ones? Its about the same amount as it does with POS.
The problem is NOT POS or POW. The problem is, that the richer are always getting more than others. It was like that thousand years ago and it will be like that also thousand years in the future, if we stick to money as THE central life instrument. The only way to solve that, is to remove the possibility of storing value at all or understand that its not needed.