I think fiat will no be worthless if ever a bitcoin will rise at that rate. In the first place, bitcoin value is in fiat. Second, not all the time you have an internet connection to be able to process all your transactions. If it will be useless, many banks including world bank will be useless too. And world bank will not let that happen.
I think the internet will be universal in the future, so there is no need to be no negative.
It is possible that internet will be universal, I heard that some countries do provide free internet for their country. Here in our nation our government is now in their plan to provide free internet in all places so it is easy to access net.
If bitcoin price will get higher I think that fiat won't still worthless since we cannot use bitcoin anywhere.