The real backing that a US dollar has is not its gold. It is the fact that the US government has declared itself obligated to accept tax payments in terms of US dollars, and it will not accept anything else. That's the dollar's base case, and the reason why coming off the gold standard didn't bring the house down is that was really
always the true value of a dollar. The gold was an illusion, suitable for an era in which people couldn't think abstractly enough to understand what the true backing was, but one that we can now be rid of. The recursion of the value of government fiat money does indeed have a base case.
This is why a government is so tied to its currency. In some sense it isn't a true cause and effect relationship, both the stability of a government and the stability of its currency is tied to the same third factor, its credibility.
"All a currency really needs to be valuable are two people who have faith in it"
Which is an equivocation game, in that "have faith in it" must itself be motivated by something at least locally rational or it won't work. I have faith in the ability of a dollar to buy off the men-with-guns who will come and take all my stuff and ruin my life if I don't pay my taxes.
All government fiat currencies are thus in fact backed by something real. I don't entirely disagree with the BitCoin community that that is a more tenuous backing than one might abstractly like, but I do not see anything in practice that would be better; value stores are intrinsically ephemeral and there is nothing you can do about it.
The reason why BitCoin is crashing is that it was built on the false premise that currencies have no backing, so we might as well create a cryptocurrency with no backing. But that's false. BitCoin is actually special in having no backing of any kind, and that is why failure is and will continue to be inevitable. The whole thing was built on a false foundation.