When you do a transaction with a credit card, the transaction is certified to be legitimate if the card #, name on the card, expiration date, and 3-digit code (4 on AMEX) all go through an algorithm and spit out the correct result.
Not having the expiration date on the card would make it less secure, because the result of that algorithm would be easier to calculate. This varies a bit with modern cards (EMV chips, tap-to-pay), but the rough mechanics of the process are the same.
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