We already had, in essence, a 'proof of work' system with gold. Gold supply increases by only a percent or two per year, and it is highly resource / energy intensive. And note that many central banks, including US, China, Russia, have and /or are even adding to their gold reserves. (Ben Bernanke says it's for 'tradition' - cough, cough, eye roll, cough)
But as JP Morgan said, "gold is money. everything else is credit." Banks don't care about the underlying reserve money as long as they control the credit, which gets used as if it were money.
>but it would certainly be different.
I don't see how. And even if it were, the powers that be like things just the way they are.