I mostly agree with you that banks are hiding their victim status but I think your framing is too intense. The magical idea of identity as an intangible self isn’t helpful.
It is bank fraud and imitation with the intent to abuse the reputation of the person imitated. It should be illegal to imitate you when it negatively hurts you. It’s illegal to imitate police and doctors etc because it uses their reputations for fraudulent means. This is the same thing.
Banks are the financially defrauded victims in this situation, but the victims are also individuals because banks passed the reputational risk of fraud to the customers. If your credit score is hurt and you need to hire lawyers to fix it or you get denied for a mortgage (or just a good rate), you’ve experienced tangible harm.
Banks know they experience harm here. They plan for it. It’s baked into the prices and financial statements. Read the essays by Patrick McKenzie, he’ll argue that fraud is intentionally tolerated. They know that the consumer won’t be expected pay once the fraud is discovered. That’s not their goal, and they’re not being deceitful here.
You can argue if this system is overall good or bad, but it almost certainly has led to cheaper credit for everyone. Outsourcing credit worthiness to a magic national number (or 3) is cheaper than every credit union assessing risk themselves, with less knowledge.