In particular, I think a mixed economy half run by the state, half free markets works pretty well.

There is no contradiction between Bitcoin and the existence of a state. There are lots of ways of regulating and taxing. Sure, Bitcoin might change the details of them - that's just growing pains.

e.g. I would make it compulsory for any company granted limited liability to register the public keys of all Bitcoin wallets it has the private keys of with the tax office.

Or, if necessary later because that's too hard to track, tax either land or carbon emissions directly (rather than income or exchange of goods).