They only have value above their utilitarian value because people say they do.
Two major differences between precious metals and fiat currencies are:
* The utility value for fiat currencies is zero for book-entry money, almost zero for paper/plastic currency, and that of base metals for coinage ("melt-down value"). The utility value for gold, silver, and most other precious metals is at least as much as base metals, there's just a lot less of it to go around.
* precious metals have a known, reasonably-predictable caps on long-term future supply based on active mines and known deposits (subject to technology disruptions such as what aluminum went through in the 19th century). The "future supply" of fiat currencies is about as predictable as politics. That is to say, it may be reasonably predictable in the short- or even medium-term but for anything longer than a decade or two, the political risk can become significant even in countries that currently enjoy stable govermnents, stable banking systems, and stable currencies.
I'm leaving out the difference that fiat currencies are typically legal tender in their country of origin. Precious metals might have been legal tender in the past, but I can't think of any major country where they are legal tender in any practical sense of the word (that is, the are legal tender, AND when you pay your debts with them you are credited with the current spot price of the metal in your local currency, or at least something very close to it).