There is no doubt that we will start seeing a lot of governments issuing there own currency in digital format. Even countries like India is planning to issue a digital version of their own currency which will be known as digital rupee.
Sadly government controlled digital currencies will take over the Fiat market slowly but steadily in near future. But I would not call them as cryptocurrency, rather they will be just a digital representation of centrally controlled Fiat currency running on a private blockchain.
Remember, the rules of a private blockchain can be written for their owner's benefit. Probably the government will allow every Bank branches within their country to act as master nodes to maintain the scalability of the chain.
Technical challenges and the possibilities are a different story all together! But government controlled digital currencies will certainly take the centre stage of the economy within a few years of time.
One way or another, governments will issue their own digital currencies within the not-so-distant future. The inception of Blockchain technology, has caused many governments and central banks to explore ways on how to improve the existing monetary system. It's been proven that Blockchain provides unparalleled security and efficiency towards worldwide transactions. Despite its many limitations, we're getting one step closer towards experiencing a transition from physical to digital cash.
Which is why, it's becoming evident that government-issued cryptocurrencies are the way of the future. Somehow, central banks worldwide will adapt to an existent blockchain (either Ripple, IBM's World Wire Blockchain, or Hedera Hashgraph) or one of their own in order to distribute the new government-backed digital currency. With many countries devising their own solutions (India, China, and even Russia), it looks very likely that we won't be using physical cash anymore.
Nonetheless, this will take some time before it becomes a reality since many people are still accustomed towards using physical cash. Old generations will find it hard to adapt towards the new monetary system, while that won't be the case with new generations (millenials). Not to mention, there are some countries worldwide which lack Internet access. Which is why, I believe that the progress of implementing government-issued digital currencies will be a slow and steady one. Just my thoughts