Banks can't work with bitcoin, search "fractional reserve". Banks may offer some Bitcoin services in future but it won't replace fiat services nor it will be possible to seamlessly juggle/ exchange between bitcoin and fiat.
That is true, banks can't fully operate on Bitcoin or any other cryptocurrency and fiat currencies will keep their position. But that is not the goal of Bitcoin or the banks.
Still I think banks will start to offer Bitcoin connected services to their clients because they are well aware this is the future and potential good source of profit.
One of the important obstacle to go live with such services is lack of regulation and position of central banks but I think this will also change in the future.