Gold: Variable cost to find, mine, and refine.
Fiat: Fixed cost of a standing army to protect the ability to print 0 variable cost money.
Bitcoin: hardware capex and electricity opex needed attributed as variable cost to make more money.
A fair monetary system is one that:
  1. Minimizes Seignorage (Value - cost of money)
  2. Attributes Seignorage via a free market, decentralized competition
Fiat having 0 variable cost means that overtime the dollar doesn’t store value. Under a fiat system: Medium of Exchange: dollars Store of Value: houses (or assets) as collateral for credit
Fiat steals the ability for a person to save their time without taking investment risk.
Fiat which is poofed out of thin air is not Proof of Work
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@pony agreed there is no variable cost to make more fiat. However there is a fixed cost (aka Proof of War) to maintain the god like power of creating money from thin air.
The idea I have is that all money has a cost, including fiat, however it is important to note whether the cost is variable or fixed when creating more money. If the cost is only fixed the system has misaligned incentives.