It's an interesting thought. Various banks holding their own blockchain records, adding blocks, ... How do the current international banking records actually work? There must be some way to achieve some confidence that the other party did not just make up the "money". OK, banks "make up" money all the time, that is how the financial system works, but there must be some ways to have shared trust already. What are they?
If banks were the trusted parties in a blockchain, then how would two customers change funds? Need to send the transactions to a bank of choice to be included? If they have different banks, how long would it take for their chains to sync the transactions? Or is it just a single chain? How are the blocks verified across? Hold a key ceremony (swap party time) and all "banks" exchange keys they later use to sign the transactions and blocks? Give each customer a key to use? Obviously you don't need miners to hash stuff, just signed by the parties? How is this different from the current system again?
It seems this could be made to work. But I have not yet seen a working system, or an explanation of one of this kind.. One that would explain the special benefit of blockchains in this, and their exact role that makes them special, or the overall resulting system itself.
With Bitcoin, XMR, and various "shitcoins", it is quite obvious, since the idea is to decentralize and avoid the banks. Since avoiding the banks is the ultimate goal they had, this makes the questions even more interesting..