> Fiat money has value because it is widely, almost universally, accepted in exchange for things of intrinsic valueNo, technically fiat money has value because it is accepted by a government to settle taxes. Which is why it loses value dramatically when a state collapses or otherwise becomes irrelevant to the local economy. Because traditionally the state itself was the issuer of such currency, already we have a massive conflict of interest at the very start: when the state pays out his own debts in its own currency, it's effectively asking his creditors to believe that currency has some value in the real world, while also telling them exactly how much that is supposed be. To "solve" this problem they invented central banks, which are supposed to keep governments away from the process of determining the actual value of a currency, if you believe that they are as independent as they proclaim. In the end, what matters is that enough people believe that certain arrangements are fair, and that the government will still be there tomorrow asking them for taxes. As long as that's true, one might well use the currency as a unit to settle private trades too, but that is a consequence of the original belief.
> I'm not aware of any non-government-backed fiat currency which has gained widespread use in the history of humanity
The key in this sentence is "widespread", which is something you can redefine pretty arbitrarily and hence move goalposts as required. In practice, other tokens have been used here and there, but in the end, what wins tends to be government-backed tokens for the simple reason that authorities will always enjoy a right to put you in prison if you don't settle your taxes in the currency they desire.
If you look at it from a technical perspective, any collapsed state where the local currency has been wiped out and internal trades are settled in USD or EUR (a pretty common occurrence), in practice is already using an non-government-backed token, something on which nobody in the local economy has any control. To these areas, it doesn't really matter that the USD will be accepted by the US Federal Government to settle taxes; they just need a unit, and since this unit is accepted at the fringes of their system, well, might as well use it internally too.
> Being able to spend it is the "killer app" of cryptocurrencies
No, being able to convert into other tokens at the fringes is the killer app. Which quite a few cryptocurrencies do have, although in an extremely fragile state. The longer they keep them up, though, the easier it gets, as more and more people believe that the underpinning arrangements are fair and exchanges will still be here tomorrow to exfiltrate value to prison-avoiding currencies.