I don't think that's true, that the economy was less stable a century ago than it is now. People used to give out 50 or even 100 year bonds, and recessions usually were not as bad and didn't last as long.
But even if I'm wrong, the currency not being based on gold is only one of a billion other things that has changed in the economy since then. It's a completely different world.
And while bitcoin is not a national currency it has the potential to become a universal currency online. People could work for bitcoins and use them to buy what they need online from other people that accept bitcoins. The currency could circulate through many hands without ever once being converted to another currency.
And since it's online any conversion could be done quickly and automatically so the effective difference between holding two different currencies wouldn't really matter. The only thing you would have to take into account is how likely they were to increase or decrease in value in the time that you aren't spending them, and bitcoin has a clear advantage in that regard.