” That happens because gold production doesn’t keep up with the economy”
Gold production does not need to “keep up” with the economy. you are mixing the concept of a gold standard with that of fiat currency that expands money supply to hide the devaluation.
A dollar having a fixed purchasing power can cover any expansion of the economy.
Absolutely correct. Imagine if the money supply (gold) was effectively fixed, or expanded only with new mine supply. Increases in productivity and technology would not be "stolen" by inflation (that only government and debt-issuing financiers), rather those benefits would flow to the masses of workers and American consumers, as prices would naturally decline reasonably and steadily. A middle-class person's real wages and savings would increase steadily. That's why America boomed in the 19th and early 20th century.