Satoshi meant for the same thing when developed bitcoin, people working and earn money still being able to prove their ownership by POW.
I think it is owning the privatekey of the address that can serve as prove of ownership of Bitcoin since we cannot store it in our computer but can have the privatekey in order to access the bitcoin on the bitcoin address.
We don't have anything called as real money that could have value on it's own but we provide a token/paper/coin/item that is the proof of work.
I also do not think token/paper/coin item is a proof of work as the way you wanted to tell us, I guess it is a proof of representation of the value those items are presenting. I might be wrong in this though
In traditional economy nothing is fair, someone could earn $10k just by doing 80 hours of work sitting on their a**es while someone else could only earn $500 doing even harder work in same amount of time, in bitcoin mining though everyone is doing the work equally and earns equally and if they want to earn more they'd work harder than others. this is the concept and is the fairest way of distribution of wealth.
There is nothing fair in this worlds system. See how prey are being eaten by predators without them be able to eat them back. It is the survival of the fittest, those who can adopt and adapt in the environment will survive . Same goes with markets.