because Proof-of-Work only generates value for an arbitrary, made up coin if it has no other real value.

Otherwise you're making money that way, and the value of the coin is tied to the work that you did.

until recently gold was a pretty but mostly useless metal. too heavy for practical uses, too melty for industrial uses, too soft for weapons, etc. but it didn't rust and was a good medium of exchange because it had no other real value. once it has value outside of being currency it's less useful in that capacity, since now its value is tied to how much you can get for it by utilizing it in computers, chemical reactions, etc.... same basic idea with PoW