A single government backing cryptocurrency will create a huge disadvantage for the others, and other countries will be forced to do so but why on the first place any government will back it?
A government that decides to back a crypto currency can create enormous wealth for itself.
We have seen that small countries have benefited a lot by lowering their tax rates.
On face having near-zero tax rates makes little sense for a government, but tax havens are done themself a lot of good by lowering taxes.
In the same manner, small countries can benefit a lot by backing or launching their own crypto currencies. They may lose some control over their monetary policy by backing a crypto currency, but they will get back a lot more from increase in value of that currency.
The country can either corner a big chunk of the currency before making the announcement or pre-mine a new currency and then launch it.
For example, GDP of Cyprus is around $19 billion. The market capitalization of bitcoin is around $17 billion. Both are of comparable scale.