> Bitcoins have intrinsic value if they enable desirable interactions that are not possible without them.
Yes, any fiat currency has the 'intrinsic' value of enabling some kinds of interactions that are not possible without them. For example, hard-to-counterfeit pieces of paper have an intrinsic value. The problem is that such things are often substitutable: the real value of most paper currencies comes, circularly, from the fact that we've decided to settle on this set of hard-to-counterfeit pieces of paper, not a different one. That's why it's fiat currency, because its value as currency fundamentally derives from the fact that people have agreed to use it as currency.
The same applies for Bitcoin; the general idea could be a good one, but Bitcoin is not the only possible implementation. If we settle on this implementation over others (perhaps because it was first), it is for reasons closer to fiat money than for reasons advocated by "hard money" proponents that they have value.