One step that can be done by the Bank is to allow Bitcoin transactions on condition that they have to be registered on a special platform. Later the patform must be accompanied by a central bank permit.
This means that all bitcoin transactions must be recorded by regulators, now there are many illegal bitcoin transactions without permission and without supervision from regulators.
I agree that Bitcoin can be more efficient than bank transactions. However, the banks have no say in approving Bitcoin transactions. They can only limit or monitor cash conversion to bitcoin and vice versa. That's it. Once you have bitcoins, you can freely transact via the Bitcoins network and the banks can do nothing about it, neither allow them, nor prevent them.
Thats why OP says that banks will allow transactions of bitcoin with condition of registering on special platforms.so before hand this is not happening ..
For me crypto transaction is more accurate,more efficient and more cheaper than banking networks so I believe that in short time this will happen,since banks are now starting to adopt blockchain to their technology