Yes, it could be worthless, but it would take time to achieve this... many people still will continue to use fiat money for many years, before that happen.
Indeed fiat has been existing for very long right now and they have a very big foundation which you can't just hit trough.
For fiat to be worthless there needs to be a big chain of events in alot of years or else it will not happen at all. I don't think bitcoin could make fiat worthless.