The confidence is not in the currency or the central bank.
The confidence (of the markets) is that the central bank (on behest of the government) will use currency as a tool in order to ensure that economies dont sink due due to negative outlook on the future.
There is nothing stopping central banks from creating their own cryptocurrency and controlling it by controlling all the mining (and hence being able to change the rules of deflation/inflation set into protocol). In fact a "bit-dolla" could probably be used much more effectively as such a tool since everyone would know what everyone else has as blockchain is public. Would these banks have gotten "too big too fail" if their "wallet addresses" were public?