I think it's more to do with agreements with the bank. They need to show they have fraud protection measures in place, and one of their agreements is that they physically see the card that the booking was made with. Otherwise if there is a dispute from the cardholder, CX will be liable for the charge and will not receive the cash from the bank if they don't have these kind of measures.

It's a pain as I've also had the case where the card I used has been cancelled before I took the flight. The usual endgame if you can't present the card is that they will credit back the original card and then make you pay the fare again before boarding.