Banks are already paying for servers to process and store information.

Yes

A few validators or collators (quite cheap for a private network) provided by several banks would cost a fraction of what they pay now

How? They'd be doing extra compute work for no reason (validating already valid transactions), and storing extra data (lots of hashes) for no reason, so it can only make infra costs more expensive. Plus the added complexity meaning you have to hire an extra team just to understand it.

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

That speculative world as shitty as it is, is the only proven use case of the technology, if you take that away then blockchains are even less useful