Yes, but if we are talking about a private permissioned blockchain, there’s no need to obtain returns from staking. It can be even a Proof of Authority tokenless network for what banking care.

Banks are already paying for servers to process and store information. A few validators or collators (quite cheap for a private network) provided by several banks would cost a fraction of what they pay now and they’ll keep owning the data, they could reverse transactions, be covered by several layers of public encryption, guard the user’s wallet/login, etc.

Don’t mix blockchain with the speculative world built on top of it. That’s only an unfortunate use of the technology.