Depending on your jurisdiction, that may not work. the payment authorisation is legally distinct from the contractual obligation to pay, and cancelling one does

Depending on your jurisdiction, that may not work. the payment authorisation is legally distinct from the contractual obligation to pay, and cancelling one doesn't cancel the other. Of course, most companies will give up if you cancel the card, but some will threaten to send round debt collectors. There do need to be some laws about what companies can write into contracts about how to cancel.