One problem with this (and a common misunderstanding of crypto as an "anonymous currency" by the general public) is that it would allow everyone to see exactly

One problem with this (and a common misunderstanding of crypto as an "anonymous currency" by the general public) is that it would allow everyone to see exactly how much money everyone else has in their accounts, what they're spending their money on, etc. With Bitcoin there's at least a degree of pseudonymity if you're careful about publicly linking your wallet to your identity, but I could imagine that's not really possible for state-sponsored currencies. Having a cryptographically verified history of everything my government is spending on would be cool, but due to the nature of the distributed ledger it would require private citizens be put under the same microscope. At least with the alternative of one central bank controlling one central database, there's some degree of restriction to personal information (I'd imagine the bank wouldn't let any average Joe request ledger data on their neighbor just for fun, but public interests would be fair game).