> But as a 'fiat' currency, it lacks the institutional backing of other currencies such as the USD

This is not what "fiat" means in monetary econ. USD is a fiat currency (meaning it is backed by government "fiat," which literally means "a formal authorization or proposition; a decree."

BTC is currently only currency at all in limited contexts, but it is difficult to classify in the established categories of money and fiduciary media. The bucket it gets closest to fitting into in how it works, given that it is not backed by anything except its own perceived value? Commodity money. That seems off, of course, since most (though not necessarily all) historical commodity moneys have had a clear, usually industrial, value, and commodities have traditionally been only physical (though that seems to be changing). Some economists are suggesting "synthetic commodity money" as a category for this, but we're still in the early days.

"But," you might reply, "commodity money has a price floor above zero that 'backs' its value." But while that's historically true (see note), it's not clear that it matters. Cryptos designed to be used as currencies are certainly bubbles through some lenses, but through the same lenses all commodity moneys look like bubbles. An economist friend discussing this with me around ~2013 pointed out "money is just a bubble that doesn't pop."

Say a precious metal commodity money trades for $1500/oz, but through a complex model economists estimate that its industrial value would be $100 if it weren't used as a medium of exchange (or speculatively, as a number of commodities like gold are held). A cryptocurrency, on the other hand, is trading for $1500/unit, and its price is estimated to be ~$0 without such use. One has a price floor of $100, and a "bubble" value of $1400/oz, while the other has a price floor of $0, and a "bubble" value of $1500/unit. Does that distinction make a difference? It's not actually clear.

It's certainly possible to imagine a cryptocurrency reaching a long-term equilibrium where it is considered valuable because it is a well-established medium of exchange and has reliable purchasing power. Imagine that someone has created this, and it happens to have the best money qualities (durability, portability, etc.) of any currency ever, plus great UX. How would it get there? Well, there would have to be a fairly drawn-out period of speculation where the value fluctuated pretty wildly as the market attempted to find an equilibrium based on future expectations of its value.

So cryptocurrencies now are behaving exactly as we'd expect them to behave if they were to one day become "synthetic commodity money." The question is whether any of them can actually find that equilibrium. It may not be possible to bridge that gap, whether because the fundamentals just don't work, or because the fluctuations are too strong to ever create a real equilibrium, or because the US or China finds a way to shut down any crypto that gets close. But stranger things that seemed less intuitively plausible have happened.

Note: usually -- there are some historical moneys that don't fit clearly into this paradigm, such as cowrie shells, of which the use in jewelry looks to have been more of a symptom rather than a cause of the value*