I don't think that fiat will ever become worthless even price of bitcoin reaches to the moon as everyone is dependent on it for living and even if we have to use bitcoins we need to convert them to fiat first to spend them.
If bitcoin price reached $10,000 then definitely we can see a massive conversion of bitcoin into fiat.
Now if fiat is worthless when that day comes, then no one will convert and it's useless now for a dream price since all in all 1btc=1btc.
Bitcoin is all digital, Exactly.
That is why Fiat is never going to be worthless,
It is really hard to buy food with bitcoin, especially if there is going to be a crisis etc.
Also fiat is controlled by the government, while bitcoin isn't.