It wouldn't be a true cryptocurrency if it was backed by a government because they would have the power to set inflation and seize coins if they wanted. Maybe it could work if it was truly decentralized and you were in complete control of your funds but I'm still skeptical. Why use government currency when we have money backed by the people.
Government crypto currency doesn't exist and will never be exist, they don't support crypto and that there's no way for them to like it as well.
I often said this, how can a single government can start its own currency. And lets suppose they do; the restricted number of users would use it and there wouldnt be much obvious change in economy of the country.