what if they pay using a stolen chequebook?
how are you going to chase that up?
We keep all the customers details first when doing a repair for them (PC repair shop) and then check the cheque is made out from the right person, as well as checking they have the associated card.
You're right though, it's possible one could slip through the net. I guess it's a risk retailers have been happy to take as opposed to alienating customers by not accepting them. Times have since changed however.