Your whole argument is based on gold not as money, but as an asset valued in fiat currency.
No! It's not the fiat-currency-price of gold which doubles and halves, it's the real price, the only price that matters, the amount of goods and services which you need that you can purchase with it, which is the only real way to value an asset. (It's one of those terms of art in economics that actually means exactly what it says on the tin.)
And the amount of gold may be stable, but its value is not. You don't hold gold because of its intrinsic value. If no one else wants gold anymore you will not benefit from its intrinsic usefulness by turning it into pretty jewelry or using trace amounts in the manufacture of electronic components. You hold it because it has an effective value, because people demand it, and that demand is just as artificial as the demand for the "fiat" US Dollar, which is a bedrock of stability in comparison. For all the laser-focus on the supply side, gold-bugs have lost sight of the other half of economics, demand.
Oh, and fun fact: You can convert between fiat-currency price and real price using Math. The typical math involved is a little thing you may have heard called the "consumer price index" that measures inflation. In its worst year ever, US dollar inflation once hit 14.76%. Of course that kind of yearly change from gold is just business as usual.