Well, a physical dollar bill has intrinsic value as well; if nothing else, you could burn it for energy. The intrinsic value is a minuscule fraction of the "official" value, but still nonzero.
The intrinsic value of gold is a lot greater, but probably still only a small fraction of its general market value; its very reputation as synonymous with tangible wealth serves to paradoxically inflate its value.
And the Deutsche Mark made great wallpaper. The intrinsic value of an object created for a lost purpose is worth less than the materials it's made out of.
Gold, on the other hand, has a naturally limited supply and has notable uses. It's reputation as a symbol of wealth is not only because of the cost, but also because there's not enough for everybody. If there was a limited supply of denim, we'd see a big comeback in Storm Riders.
It's like owning a Tesla - it's not just a $100k car, it implies that you're a somebody.
The intrinsic value of gold is a lot greater, but probably still only a small fraction of its general market value; its very reputation as synonymous with tangible wealth serves to paradoxically inflate its value.