In the old days, the contract was part of the signature card. You can look at images, but the contract was intact.
Many years ago, there was a fraud, where an account was being syphoned-off. All of the signatures on the withdrawals were the same, but none matched the signature card. All the tellers (but one) processed the transactions. The lone teller was placed under surveylance.
Before lunch one day, the suspect teller went to the signature card cabinet and was seen swapping cards. She took out the original signature card and replaced it with a card with the same account name and number, but a different signature. While the teller was at lunch, her friend came into the bank and made a withdrawal from the account writing the accountholder's name in her own handwriting. When the teller came back from lunch, she swapped the fraudulent card for the original (- except, she was caught with both cards.)
That may be one reason not to have cards lying around.
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Integrity. With it, nothing else matters. Without it, nothing else matters.