If civilisation falls, how do "pre-1965 silver dimes", or anything else of little practical value, acquire that role?

It's simple; gold and silver are schelling points. They have been used as mediums of monetary exchange for literally thousands of years. Maybe if you're in a malthusian scenario where people are starving in droves and the survivors are spending every available minute working to stay alive just a little longer, gold and silver won't do you much good. But as long as any kind of economic surplus exists, it's a pretty good bet that people will be willing to trade for gold and silver, if for no other reason than because they think that other people will also be willing to trade for gold and silver.

In a world where there are generally accepted forms of money, I can rely on that general acceptance to safeguard the value that I store as money.

The "general acceptance" provides you with liquidity but it offers no guarantees at all about the value of your banknotes.