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.

Horribly wrong, I'm afraid.  You are confusing the concept of money with the concept of tokens.

In your example, the notes aren't valuable except as they embody promises that they can be redeemed for stuff, that is, they are tokens.

Money (in this context) is something (either actually present or in token form) that is widely accepted in trade.  Doesn't matter much what the thing is, or why it is widely accepted, just so long as it is.

Kiba is right that regression isn't important here.  I would go another step and say that regression wasn't ever important anywhere.  Money was in wide use all around the world for thousands of years before anyone thought they needed to invent a story to retroactively rationalize how it happened.

For bitcoin to be successful, it just needs to be better than the alternatives for at least one use, and I'm sure each of us can think of several things that bitcoin does better than any existing financial system.

By the way, discussing this sort of stuff is really hard.  When we say money, we are usually referring to a token (cash in the wallet) or a token for that token (checking account, etc), or something even further removed (ATM card/check/savings account).  For extra fun, as we peel away the stack of tortoises, we find out that the bottom token (cash) isn't a token for anything.  It is just a token. 

Yup, exactly.  USD are the best, most useful empty promises on the planet.  And they've been empty for nearly 100, 80, or 40 years now (depending on your point of view), and the world hasn't come to an end.

I've had the "money is nothing" chat with many people, and I always know when they "get" it because there is always a look of absolute horror on their faces at that instant.  And always there is a call a few days later, or a few weeks, when they work through all of the repercussions and come to the conclusion that you can't possibly run a global economy on empty promises.  Except that we clearly are doing exactly that, and it works.  More or less.

That is why bitcoin has such a low barrier for success.  Value is meaningless, the key is utility.

But you are forgetting two things:

1. Bitcoin and USD are opposites. The USD is a fiat currency while Bitcoin is a voluntary currency.
2. You are misrepresenting the position of the people criticizing fiat currencies. There has not been a paper fiat currency that has lasted more than a 100 years in history. And paper fiat currency is a very old concept, it has been tried for centuries. That means something.

And we can see the effects of the monetary policy all around us. Bubbles everywhere, big disparities in wealth, destruction of the middle class, etc... The fiat monetary system is hurting us. But that does not mean that you change to a paper fiat currency and the next morning the whole economy collapses. Nobody is saying that. The market is resilient and can keep going even when abused. The system could have another ride and last 20 or 30 years more, who knows, but its quite clear that its getting to the end. Its more and more unstable as time goes by.

1.  I'm well aware of the difference.

2.  No, I haven't misrepresented anything of the sort, mostly because I haven't said anything about people criticizing anything.  I'm also well aware of the history of paper money.

Generally speaking, people that know enough about our monetary system to criticize it don't need me to explain basic concepts like what "backs" the dollar.