Any country can move to cashless society but I think there is still a lot of time left for it to happen. Cashless society does not mean that fiat currency will end completely. And by cashless society it would also be wrong to imply that it will be cryptocurrency only.
Every government wants a system where the government can control anything it wants so if we view this in this way then it will never gonna fully happening. And I think fiat currency is still important for political action and increasing connectivity with the global economy, it's not going to end easily. However, it can be expected that in the future, 100 years or less, the economy may become dependent on crypto currency.