This is not quite accurate historically.
The gold standard was a promise from the monetary authority that they would exchange banknotes for gold, or gold for banknotes, at a fixed ratio: such-and-such a weight of metal in exchange for paper with certain numbers written on them. This did limit total money creation, but not at a one-for-one rate only when people deposited gold.
Central banks can, and did, make other kinds of asset purchases with their own banknotes, without using those newly issued banknotes to purchase gold.
But the promise was that those newly created banknotes, used to purchase (for example) government bonds, could then immediately be returned to the issuing bank in exchange for gold, if the holders so desired. So it was necessary for a monetary authority, on the gold standard, to limit its outstanding banknote liabilities, even with non-gold purchases of assets, lest a large amount of people holding banknotes would show up simultaneously and all demand gold collectively, thereby draining the monetary authority of its gold reserves.
Trying to go onto a gold standard today would have immediate, and extremely large, effects.
If the Federal Reserve tried to peg gold at its current dollar value, then people would immediately rush to the various reserve banks and demand gold in exchange for their banknotes. But the Fed simply doesn’t have enough gold in reserve, at current gold prices, to sustain such a rush on its reserves. It would almost immediately run out of gold, and therefore the standard – a promise to exchange banknotes for gold at a fixed ratio – would immediately end.
An alternative would be to fix the dollar value of gold at a level high enough that people would rather deposit gold at the Fed, in exchange for newly issued banknotes, rather than take gold out by giving up banknotes. The problem is that this would require an extraordinarily high dollar price of gold that would immediately, and vastly, increase the current banknote supply.
It would be massively inflationary. People with gold would deposit that gold at the Fed and receive banknotes at a price vastly in excess of the current market price of gold, and therefore they would receive an extremely large number of banknotes in exchange for that gold. And then they would immediately spend those banknotes on stuff, hopefully before prices shifted upward to destroy the purchasing power of their newly received banknotes.
The only way to make a real transition to a gold standard would be a gentler, slower hybrid system. The Fed could introduce a new parallel currency backed by gold which circulated freely with the current fiat currency, but not pegged to the old currency. This new currency could, at first, have an extremely volatile exchange rate with the old, but perhaps with the hope of stability over the course of time as Fed influence slowly stabilized the price of gold against the rest of the real economy, dampening down the current wild volatility of gold prices. After the price of gold was stabilized against other goods and services, the government could then transition to using the new currency as it slowly removed the old from circulation.
But it’s hard to see what the point of this would be.
The gold standard failed in literally every country. The political equilibrium obviously points toward continued failure. Intelligent monetary cranks today favor massive deregulation of the banking industry instead of a new government-sponsored gold standard.