That’s not what I was taught as a cashier, or what I taught my cashiers as a Supervisor when I worked in retail. We were to always check the signatures on the cards with the signature on another form of identification.
Checking signatures, yes. Taking driver license #’s and such, if I recall correctly, wasn’t permitted.
Checking signatures, yes, but from the card to the signed receipt. This may have changed, and maybe it changed before you worked as a cashier.