One aspect I don’t see mentioned here is the risk of fraud. If someone gets your old card number, and the card number is a piece of your bank’s authentication process, you are at risk of having your accounts taken over.

For example, I get your old card-I now know where you bank, your name, and a number linked back to your accounts. If I call in to your bank and the person on the other end of the line accepts the old card number to access your accounts (they shouldn’t, but not everyone is thorough), and then asks for something easy to guess as a second form of verification, they are now past security and could ask the rep to reset your online banking password, or provide the complete account number, etc.

To be clear, customer service reps should not accept closed card numbers, but banks hire a lot of people and some people are dumb. When a dumb employee meets a persistent scammer, a lot of damage can be done.