When did I say it can't work? I said you're still on the hook for charges to your card. Specifically, if a service is provided, even if you cancel your card.

It doesn't come up often, because most places charge you before providing a service. For example, if you have a NYT subscription, and it goes to renew and your credit card has been turned off, you don't actually get your NYT subscription. No services rendered, no accrued charges.

However, if your gym bills your credit card at the end of the month of your membership, then you are still obligated to pay it, even if your credit card has been disabled, because the service has been provided.