But these are two entirely different utilities (the latter is not related to the concept of money as such)
Utility of money comes from utility of asset that represents the money, can't separate one from the other. For the average person the difference is not distinguishable. Can they make savings and be sure they can purchase the same amount of goodies at the end of life is all that matters to them, and fiat doesn't cut it. Nobody can argue with a straight face that fiat is good at preserving retirement savings. Wait, politicians can. When is a politician not telling lies, when his mouth is not moving.