Paper money, in most countries in modern times, has been a
more stable store of value than gold. Consider, for example, the price of gold over the last 10 years - the run up to $1700, the fall below $1200, the small recent recovery. Has that been because of the change in value of the dollar? No,
most of that change is in the value of gold, not in the value of the dollar. That's not a very stable store of value. Even the Swiss Franc has been more stable, despite the recent shock.
Paper money has mostly been a more stable store of value than gold... except when it hasn't. When the paper currency becomes toilet paper, gold looks like the perfect store of value.
The modern role of gold, then, is more insurance than it is a store of value. (Or you could think of it as a short on currency.)