No, it doesn’t give value to the banks. Banks only have value because you can use them to store and borrow money which has value. Your theoretical bank has no v

No, it doesn’t give value to the banks. Banks only have value because you can use them to store and borrow money which has value. Your theoretical bank has no value because your theoretical currency does not, either. FDIC insurance reinforces the value that banks (and the currency one can access through them) already have.