If we can regulate them, so can the government. AFAIU Bitcoin is designed to prevent exactly that, at least in general. Fully resolving their books would requi

If we can regulate them, so can the government. AFAIU Bitcoin is designed to prevent exactly that, at least in general. Fully resolving their books would require knowing identities of those entitled to receive Bitcoin from an exchange, as only one example, as otherwise an exchange could simply transfer the right amount to an account under their control and use those Silk Road-style money laundering schemes to transfer it to some wallet they actually care about. To make sure the outlays went to the customers it's required to know which Bitcoin wallets belong to said customers. Are you going to sign up for an exchange that maps wallet IDs to customer identities for public transparency purposes?