Bitcoin will never replace fiat currencies issued by a government, such as e.g. CHF or USD.
For that, it’s missing some crucial elements, both technological and political.
For example, it lacks something like a government-controlled money creation process, which is essential to economies as we know them today. It also simply doesn’t have the technological capability to replace the amount of money currently floating around. Big Ern wrote a good article about it here.
There are some advantages in having an own government-issued crypto currency, however.
For example, if a government wants to launch a full-out negative interest rate policy (“NIRP”), everybody would run for cash. But if there is no cash, only a digital currency, then people wouldn’t be able to hoard physical cash anymore. And if we look at the enormous public debt that countries have been piling up, there are two only ways out of it: default or inflate. Default might actually be the better option, offering the chance of a fresh beginning. But politically, inflation is more convenient. And with Bitcoin, it is not possible to pursue an arbitrarily set target inflation rate.
For these reasons the blockchain technology will probably be used by governments to create their own crypto currencies, but they will not use the existing coins. Governments might actually try to ban Bitcoin if it starts to seriously interfere with their plans and activities. That might sound far-fetched, but don’t forget that not long ago, it was forbidden for private persons to own gold in the USA.
Personally, I treat Bitcoin as digital gold, though its easy tradability gives it some characteristics of a currency, and think that it is here to stay, tolerated by governments as an alternative way to make payments.