Every business needs to adapt to changes and challenges like this. Im pretty sure banks are already finding ways to join the bandwagon.they will surely profit from it. It would just be a matter of time until they accept bitcoin deposit and withdrawals.
The business needs to update according to technological upgrade but that does not mean that banks must be involved in the crypto market and i am sure they will not accept bitcoin, it is specifically made to transact fiat currency and they are under government regulation and why would they want to accept it unless the government accepts bitcoin as a legal tender it is not going to happen.