Even with my view that bitcoin might not totally replace fiat, I think that your analogy with fax machine and internet on one side and fiat and bitcoin on the other side does not correlate. Fax is what is consider now as old fashion because internet has totally replaced it, in fact not even internet but computer has taken the roll of the said fax functions.

As for fiat, it is used currently while bitcoin is yet to be accepted, bitcoin as it were, plays the digital roll for just few people. So the comparison isn't adequate.