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.
Above mate has made a perfect statement at the end that world bank will not let it happen. Internet connection and the technology will improve with additional features but the price of bitcoin reaching $10000 and making fiat worthless is not realistic. When bitcoin reaches $10000 the opposition from banking sectors as well governments will be big which might even pave path to destruction.