Then there is no "your social security number" or "your identity" for someone to open a bank account against. You open a bank account and they give you a bank card and you set an address and phone number. The day you open it, they shouldn't need to know who you are, because it's a new account with $0 in it. After that, the owner of the account is the person with that bank card who can be reached at the address and phone number given when the account was created.
Get rid of centralized identity and there is no centralized identity to steal.