Sure, but what if someone steals your money by impersonating you? Here too, ideally the victim is the bank, but now the onus is on you to convince the bank that they are the victim. They are going to say you're the victim, your identity got stolen, sorry you lost all your savings!
We need to update our laws. This is not "Identity Theft", this is "Negligent Verification Fraud", and it is the bank's fault because they were lax in their verification process.