I think government cryptocurrency is not a very good idea. Because many people do not trust the government and will not invest in such a cryptocurrency.
First, states will not issue their own cryptocurrency, but their own digital currency, that is, they will be the stablecoins of their central banks. It is unlikely that they can be called a cryptocurrency, since they will be under the full control of these states. However, compared to conventional currencies, they will be more efficient, so in general their appearance will provide them with many additional conveniences.
Secondly, as a stablecoin there is no point in investing in it, they will not be profitable. It will be a state means of payment, that is, digital money.