To me, this is all brilliantly illustrative of the paradoxical nature of money. Because "money" value is a total abstraction, it only attains a valuation when the first trade is made involving any such instrument. It was Bitcoin's clear value as a transactional instrument that facilitated it's first trade; no surprises there, as it was designed to promote that behaviour.
So I'm going to try to delineate a subtlety properly: the network had a perceivable value for use as money, but the value was qualitative, not quantitative. You can describe the motivation that sold those 2 pizzas for 10,000 BTC, but you can't put a price on it. And since the notion to make the deal necessarily came before the deal was struck, I think you can reasonably conclude that the metaphorical egg in this case definitely did exist before the consequent chicken.
I can't help but reject the idea that the network, whose entire raison d'etre depended on attaining a market value, can skip Mises' step for having a previous market price (or the "value" synonym that Mises himself used) in order for it to emerge as a form of money accepted by the market. Not when the medium has been consumately designed to be used as money, and was never used for anything else.
And so I would argue that the literal opposite to the effect described by Mises Regression theorem was demonstrated with Bitcoin's entrance into the marketplace: it became money before it had any previous price value for any other purpose, precluded by it's design for the purpose of money.
This isn't my field, for sure, but here goes.
I can't think of any counter to your point "it became money before it had any previous price value for any other purpose" other than Tucker's network/blockchain gambit. How much of Mises' work would unravel (if any) as a result? (I have no idea).
On a much more mundane scale, I quibble about the relevance of the raison d'etre and designer intent, perhaps using hindsight about smart contracts and such, but you're right that
BTC certainly seemed intended for use as money. As an aside I think
BTC is working spectacularly well as money in these early days - warts and all, given that it is not propped up by government coercion, and I thus infer with relief that government coercion is not a necessary property of money.
Your notion "the network had a perceivable value for use as money, but the value was qualitative, not quantitative" is useful, but, I fear, could be applied to anything known to have been used historically as money. It would have descriptive value (good) but not much predictive value (better).
Presumably the essential property of "money-nature", if it exists, must be something external to the money itself, something purely situational/psychological/social, but then the fun begins - does it take one person, two, or a million to buy-in before the entity is "really" money? Is it still money if the people who used it as money are gone? Is it still money if a government forbids its use? Does something that is not money become money if a government mandates its use as money? On and on. Heh - let's go down to the Economics Lab and see what we can replicate.