The gold standard was far from stable - just look at the US’s economic history - it was continually swinging between inflation and deflation with regular crises, panics, recessions and depressions.

The question you need to ask is “would there generally be a relationship between the amount of gold on hand and the amount of money required in the economy?” There is no reason why the answer to that question would be “yes” over an extended period of time - you can set up some kind of sensible exchange rate at the start but it eventually (and invariably) gets out of whack.

It’s the same with fixed exchange rates, pegged currencies, etc. - these things tend to exist for a time and eventually don’t - because they’re ultimately not sustainable.