The goal of the same banks is to exclude cash payment from circulation, for this banks will use BITCOIN in the future, because even now BITCOIN provides banks with a service that people eliminate cash in favor of bitcoin. The main reason here is that BITCOIN is more manageable than cash, because BITCOIN always leaves its mark on the network, while cash is more difficult to track.
It’s no use for banks to use
BTC to replace fiat money. Think all of us heard that the world’s central banks are actively working on implementing CBDC’s (central bank digital currencies). So, to my mind, banks will use CBDC’s for the purpose you’ve wrote about.