Proof of stake is not really any different to the fiat system it's trying to replace.

If a money isn't proof-of-work then it implies that some people can create it without doing work.

Gold's proof-of-work stood it in good stead for thousands of years. It was only some of it's physical limitations that led to fiat beating it. In fact fiat would be worthless if it wasn't boot-strapped into having value by originally representing gold's proof-of-work. Now we have digital proof of work in bitcoin. It doesn't have the physical limitations of gold, and fiat is going to hyperinflate to 0 once again - but this time it will stay there.