Economics of proof of stake

Recently started getting into Bitcoin. Now I want to understand Ethereum as well. In pos the new coins will be issued for people who already owns and stake Ethereum . Isn’t this similar to rich getting richer scheme?

Some people may tell me that in case of proof of work, you still need up front money to buy mining machines. But still you need to put a lot of work to mine Bitcoin and mining is barely profitable. Whereas in pos once you have lot of coins, you can keep making more coins at very low cost. Something about economics of pos doesn’t sound right to me.

I would like to hear your thoughts.