Indeed, it is somewhat delusionally to think that if some asset in a liquid market has high volatility as expressed in a major fiat, such as the US dollar, it is the dollar that is fluctuating and not the asset.  In the relatively short term, big fiat are very stable units of account (unless something quite spectacular happens) in the sense that a quantity of this fiat represents a constant market value of commodities, whether it is bread, computers, cars, bananas, coffee, theatre tickets, or... other stable currencies.

Of course, and that was I think the essence of cryptoanarchists' remark, this is somewhat self-referential.  But in the end, it doesn't matter.  If you can buy about the same amount of Big Macs, bread, tooth brush, cars, bananas etc... with, directly, or after exchanging it for another currency, it HAS a stable value.  Because in the end, value, that is an amount of Big Macs, bread, tooth brush, cars and bananas.

In the very long run, fiat currencies are less good units of account ; but then, not much is, because the notion itself of "same value" in remote and totally different economies is ill defined.  How do you compare the value of, say, a dagger in the 7th century with something today ?

But a thing even used as a major currency, that doesn't have a price-stabilizing mechanism, will NEVER stabilize, simply because of the variable economic activity, and the variable velocity of money in Fisher's formula:

Q.P = M . V

From which: P = M . V / Q, the price level depends on V and on Q.   V depends heavily on the hoarding habits of people, and Q depends on the economic activity.  If M is a hard number, it will never be stable.  Especially if a large part of M is being hoarded, and V is very sensitive to the small amount of non-hoarded coins.

If there's a feedback mechanism from P to M, which is what central banks do, then this can stabilize P.  If no such mechanism is known, P will be very dependent on V and Q.