As I mentioned at the outset, banks take their responsibilities to protect the personal information of their clients very seriously. They do provide products and services to their clients to help ensure that their personal information remains safe.
I can't speak to exactly the economic model you're referring to of charging extra for personal identification monitoring specifically. But in some cases if a client wanted there to be more monitoring, then they should have that option to have their personal information monitored more closely. In that case, that is a product or service that a bank may be willing to offer to them.