The problem with this argument is that it neglects the consequence of specie entering and existing the market.
The California and Alaska Gold Rushes did more to devalue the money supply than anything Nixon tried. The Spanish economy of the 1700s imploded in the face of the gold glut it imported from the Incas and Aztecs.
A gold standard doesn’t stabilize the money supply. It simply deflects the question of what that money supply should be onto the private commodity market for gold. But volatility in the gold supply does happen, particularly during times of economic turmoil. And a pegged currency encourages private arbitrage, which increases the frequency of these sharp shifts in gold availability.
And that’s not even getting into what happens when you’ve got a private speculative asset independent of gold - maybe we call it real estate or company stock or cryptocurrency - that siphons off investment dollars one minute and floods the market with currency/commodity-hungry panic sellers the next. Even if you’ve got a stable gold/currency ratio, these aren’t the only two variables in your economic model.
No amount of gold changes the number of potatoes the Irish have to eat.