None of what you said makes any sense. No bitcoin isn't designed for private ledgers, it's the exact opposite, an innovation to make global, public, decentralis

None of what you said makes any sense. No bitcoin isn't designed for private ledgers, it's the exact opposite, an innovation to make global, public, decentralised/distributed (you can argue the semantics a bit here), trustless system without a dependency on any particular set of gate keepers, while keeping alive some semblance of privacy/pseudonymity. This private banking database requires none of that and is the opposite of what bitcoin was designed for. And the gigantic waste of proof-of-work is completely unnecessary, and forcing the use of it regardless by keeping a 'single server per bank' is insane, it's literally a waste of money. Not only that but it doesn't even achieve anything you want as it creates a false sense of security, after all what stops a bank from simply having more than 1 server and blowing all the proof of work from anyone else out of the water and dictating the entire database? Well guess what, the exact same thing that obviates the need for a proof of work system in the first place. Bitcoin is the dumbest possible technology outside of the context for which it was designed, in which it appears to be the only viable technology and works incredibly well. Running a private blockchain with a set bunch of gate keepers is simply ridiculous.