I think the simpler solution to the apparent disconnect between the regression theorem and cryptocurrencies is that cryptocurrencies break the regression theorem. I like Mises and all, but really? People are trying to apply the economics of the 1940s to the monetary system of today...
The regression theorem is account of how money arise from a barter economy. The theorem is irrelevant to bitcoin.
That sounds wrong, but maybe I do not understand the theorem, so lets review what I thought it was.
My understanding is that according to the theorem money arises when something useful (such as data aka information) turns out to be so useful that lots of people not only agree that it is useful but also start to use it as an intermediary in trade.
So, like, maybe once upon a time someone figured writing was so useful that instead of trading a loaf of bread for a shoelace they traded a loaf of bread either for a note saying "pay the bearer on demand one loaf of bread" or a note saying "pay the bearer on demand one shoelace".
Pretty soon more and more people were trading items for information in various variations of such techniques.
Along came computers, a new medium to write on with new writing tools, so people started trading goods for entries in databases.
And so on.
Did I get it wrong?
-MarkM-