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.
In my country (Ukraine), in a bank digital wallet, it has long been possible to transfer Bitcoin and use it for shopping. True, from this wallet it can no longer be withdrawn. In fact, after transferring to the wallet, the bitcoin itself is withdrawn from the wallet by the bank, and we have the opportunity to make various transactions for the sum of the bitcoin value in online mode. That is, the purse continues to indicate the amount in Bitcoin and its equivalent in local money.
Yes, the Russian WEB-money wallet provides for this. This is a bank e-wallet that also accepts bitcoin. It was quite convenient to use it, but in Ukraine the Russian wallet is now blocked due to problems between these two countries.
I think that this, and not only that, is also possible in the future. Banks will certainly cooperate with cryptocurrency.