1) Wealthy + Paranoid + Stupid. They'd rather keep their money in sovereigns under their mattress, than put it into any sort of productive economic activity. On a long term, especially in the US, you could pretty much throw darts and build a portfolio that competes with, or beats, inflation.
2) Conspirational: "fiat currency is a grand scheme to undermine our savings for (insert nefarious bugaboo of the day)"
3) Arguably a subset of 2) but Apocalypse Enthusiast. "When civilization crumbles, the obvious trade unit won't be something like grain, alcohol, or bullets, but my bags full of low-grade silver dimes! I'll be King of the Wasteland!"