Just as interest in the conventional economic system is wildly anti-egalitarian: very literally, the rich get richer.
Agreed but a difference is that to profit by interest, you generally have to invest, take risks, and put the money to work.
Explain? Surely stake out == stake in, or something is very wrong with your proof of stake?
Proof of stake means: your chance of mining coins is derived from how big a Scrooge McDuck style money pool you already have. Merely for owning that money, Mr McDuck gets more money.
To a certain extent, the same is true of POW as rich people can afford more hashing power.
In other words, it works like interest. In a properly functioning monetary system, interest and inflation are fairly similar, so even though the number of coins in McDuck's pile is getting bigger, what can be bought with that pile stays relatively constant.
How is that like interest? Interest is rent on money. Cash in the mattress doesn't get interest. In a properly functioning monetary system, interest is above inflation.
As opposed to proof-of-work, where the people investing in mining rigs get richer.