In effect, the dollar has this role because it is superior to both gold and to any competing fiat currency. Not only does the US have the world's largest economy, but the US is trusted to keep honest account books, is powerful enough to keep the peace, and manages an orderly, consensus-based system of international rules for trade, banking, and finance.
To accommodate the demand for dollars around the world, the US must pump out enough dollars and dollar denominated federal debt to keep the international economy running. For example, early this year, the Fed intervened in the financial markets and made massive sums available for reverse repo transactions. This prevented the markets from seizing up and caused some sharp comment about the Fed's motives. Only months later did it become clear that the international financial system was coming under severe strain from China because of the early effects of the coronavirus.
The Fed's role in actively managing dollar and dollar debt liquidity in key markets is deeply troubling to hard money advocates, which includes the Austrian school and Rand Paul. Yet neither seem to want to recognize that the defects of gold as a monetary base contributed in a major way to the severity of the Depression. Unintentionally, the gold accumulation policies of the US and France caused a devastating global contraction of the world's monetary base.
If it were possible to go back to gold as the world's monetary base, the problem of managing the supply of monetary gold would recur in new form. Gold production and monetary use and accumulation in non-monetary reserves would have to be controlled. This would require the cooperation of the world's major gold producers.
Since China and Russia are number one and three on that list, I see no end of trouble from them if we went back on gold. They would inevitably use their large gold production and holdings to menace the world economy and set the terms of economic and financial exchange to benefit themselves and disadvantage the US and other free nations.
I was long ago reconciled to this line of argument having thin appeal against the attractiveness of gold and the fundamentalist style of argument. People with little knowledge of economics and history can be easily convinced that gold is the only real money and that saying otherwise is akin to denying the divinity of Jesus Christ.