It's not as cut and dry as you want to believe. Due to automation and joblessness in the near future, most government around the world will likely adopt two major currencies. One that is the peoples currency which would likely be very similar to cryptocurrency, and the other is traditional money that'll be used for trade between countries. This will be to try and slow the rate of inflation that'll be brought from this UBI future we'll have.
But in between that and now cryptocurrency will be increasing utilized by the mid to low income people. Leaving real money for those of upper wealth. Things like the government backing your money and banks are only good if you have lots of money, which poor people lack. If you lose your job and have a hard time paying bills, then converting your money to a cryptocurrency will keep it safe.