My belief that it would go to zero. I’m curious whether “fiat is backed by nothing” proponents would disagree.
Now you might say "actually its authority rests on people with guns", but that's only to the extent that the people with the guns believe in the governments's authority to tell them who to point them at.
Underneath all is belief and sentiment.
Put another way, if people lost faith in gold as an investment tomorrow, and the value fell to the economic value of the industrial use cases, investors in gold would be ruined.
That's more than enough reason why we should try something else. It doesn't inspire a lot of confidence. By that reasoning, the USD has the same sort of backing as the Venezuelan Bolivar. So what's to stop the prior from becoming like the latter?
Bitcoin has no floor. You can only exchange bitcoin for taxes if someone wants the bitcoin.
It is the only thing the government accepts for tax payments. Given that you can be arrested for not paying your taxes it is "backed" by the barrel of a gun, a threat to your very being. In one sense this is the only real thing there is.