Fiat is already primarily (99%) represented by digital tokens with shared permission ledgers. Banks are merely being conned by developers and startups into promised efficiencies to be found with "blockchain" tech over their old permissioned ledgers or are trying to co-opt the market buzz over bitcoin.

Either way , some banks will lose alot of money and never see a return from their "blockchain" investments , others will lose a lot of money and eventually return a profit of their investments due to very slight improvements in processes, and none will be able to co-opt some of the more interesting aspects of bitcoin.