Paper notes - fiat - are anything but unbacked. It's commonly backed by the voting taxpayer being willing to go along with the taxation system that underwrites the funding of the government, including the currency the government controls.

The government systems of the US extract 35%-40% of the economy in taxation & spending obligations (inflation). Unbacked? That's ~$7+ trillion of annual tax revenue ($8+ trillion of annual spending) from the world's largest economy.

It's one of the more ridiculous myths endlessly circulated by the delusional goldbug types for pretty much the entire past century. When confronted with the facts of reality about how taxation actually works and the fact that fiat isn't actually unbacked, they always instantly run away from their premise (and I say this as a fan of gold as an inflation hedge).

Fiat is backed by a lot of guns pointed at the taxpayer's collective head, ensuring the ability to collect tax revenue from the nation's productive output; whether a given taxpayer likes it or not, whether they agree or not, whether they resist or not, it simply does not matter, the guns (along with the reach of the regulatory body) ensures compliance. In 99%+ of cases they don't even need the guns, they merely need you to understand they're always there as an option. The only thing a goldbug can do when confronted with this fact of reality, is argue that it's immoral to hold a gun to the taxpayer's head to extract taxation, which is a moot argument ultimately: your neighbors all support that virtual gun being held to your head to collect the taxes.

Those guns have very broad public support generally, meaning most of the population - in most every country on the planet - supports tax collection, by force if necessary. They may disagree on nuance, or about what the ideal rate of taxation is, however the public very strongly supports collecting taxes. There's a reason every functional nation & government uses a fairly typical tax collection system: the public broadly supports the concept and will tolerate it. And if you refuse to pay taxes, the public is generally ok with sending in the guns to make you pay your taxes as needed. The public ultimately knows they benefit in various important ways from tax collection, even if everyone simultaneously grits their teeth about paying taxes.

It's probably more reasonable to argue that the US Dollar is supported even more strongly than if it merely had gold behind it and not the guns of tax extraction. The US Government has the ability to take enormous arbitrary sums from the population (see: Covid spending), via the Fed and its capacity to 'print' as they deem it necessary. The USD has more economy behind it accordingly than it would with just gold behind it; it has probably 50%-60% of all possible economic activity behind it as needed, which is a high-end figure for what the governments of the US can perhaps take out of the economy before prompting an extremely negative social reaction. Gold could never come remotely close to matching up to that kind of financial backing.

Having backing (support) is not the same thing as saying that the dollar would retain more or less value over time if it had a gold requirement behind it however, those are two entirely different matters. The USD simultaneously has massive backing behind it, and it's going to endlessly be devalued by the fiscal mismanagement in DC.