A cryptocurrency where all the voting nodes are run by the state could fulfill the same objective. The problem is that cryptocurrencies as we know them are based upon a publicly verifiable ledger. Inevitably, the state would want an "off the books" way to move money around, which would lead to a shadow currency, and the resulting disequilibrium would destabilize either the state or the "official" currency.

Public ledger is also a privacy (and potentially fungibility) nightmare.