This is quite hard to predict about that the next century what the world will be at that time, everything is changing so quickly than the concept of digital economy would be on mainstream and I'm quite bitcoin will be main currency like at this time US$ is leading the fait world.
Ask ourselves first if we are still alive on that year. Very funny to think if what will happen to bitcoin by that year but the fact is that no one really knows until bitcoin will be alive. But the chance of no fiat on that year is possible because of modern technology and for sure in that year cashless society is already implemented but we don't if with bitcoin.