The intrinsic value of a cryptocurrency is in its utility: moving an accounted and measurable unit across the internet peer to peer.
The answer to "What is this item [the bits comprising your private wallet key] worth on its own?" is "Nothing" for cryptocurrencies, much like a 5 Euro bill is worth essentially nothing on its own. A gold bar or a bucket full of copper cents has an intrinsic value: it's metal that can be used for many engineering purposes.
That is: The value of copper is set by its industrial usefulness. Gold? Not so much.
The price of gold, in my view, is set primarily by worldwide demand for a short on fiat currencies. Even if you don't buy that interpretation, though, financial (and therefore non-industrial) demand pretty clearly sets the price for gold.
> That's a property of the network (if it works, that is), and not an intrinsic value.
The value of a cryptocurrency can be a property of the network and be intrinsic.
intrinsic, adj.: belonging to a thing by its very nature.
Gold has more alternative purposes (teeth, electronics, jewelry, etc.), but a cryptocurrency provides bookkeeping, even to some effect after its network dies. Bookkeeping, and not the assets kept track of, has intrinsic value.
I know what I'll hold on to, though, when the great blackout comes in 2022. And that's wood.
I need to think about this some more...