You forget that “precious” metals’ trading value is far in excess of their actual value. The actual use value of these metals is pretty low, in that there aren’t many uses for which they are the only option, and the ones that do exist are fairly limited.
Gold is expensive, not because it is gold, but because we have, collectively, decided that it’s valuable. In reality, it’s not. You can’t eat it, or make stuff very many intrinsically valuable things out of it. It’s not even particularly rare, so even if scarcity defined value, which it doesn’t, (there are lots of rare things that are worthless), gold wouldn’t qualify.
Certain metals are valuable because we’ve all decided that they are. Gold is as much a fiat as paper money. It’s an idea that we’ve all agreed to, and in the absence of that agreement, it’s value drops to it’s use value, which isn’t much.
The “value” of precious metals is, like the value of paper money, psychological. If you really wanted to base currency values on something “real”, you should use oil, or wheat, or something else that has some intrinsic value. Gold doesn’t qualify.