There is little need for governments to create their own cryptocurrencies, unless they want to move fiat using distributed ledger technology. A crypto euro would be a euro just like euro in any other form (banknote, numbers on a bank account etc.). A rose is a rose ...
Fiat in DLT form could have certain benefits. It could be used for micro transactions on the Internet, for instance. Banks or other financial institutions could run the nodes. Steem has shown that DPoS can scale adequately. Wallets could be implemented as browser plug-ins.