Fiat will dissapear but not the banks because they can easily to shift from FIAT to Bitcoins. Parts of histories about banks they will receive goods and merchant to be use on trade before, silver and gold as well are receivable until it become paper money or a fiat now, so it is also possible from fiat they will shift to bitcoins as long they can gain from collecting of fees and interest specially banks are already use to digital transactions in which bitcoin is a digital.