Of course, it depends on which government would support that coin, because if it is my government I doubd, that would go into it!
No matter the government that is creating the coin, there is nothing actually there to go for. Sure, I may still be trading it just the same way I trade Forex and that may actually bring about a better way to trade. However, we also need to remember that there is actually no way it would not be centralized and controlled, so holding it would really not bring about anything different from the fiat we have been holding all our lives.
It would just be the same as holding fiat then because it would centralized and controlled by the government. It may use the blockchain technology but it would be controlled then and holding it for investment purposes would not be worth it if you intend to make it as long term investment. It would be pegged to the fiat currency of the government. If I intend to invest in a cryptocurrency then it would be decentralized just like the cryptocurrencies now and maybe issued or have some partnership with reputable companies.