I don't know if the NYT does this, but with some services, if you invalidate your card without formally canceling, they treat it as ever-increasing unpaid debt

I don't know if the NYT does this, but with some services, if you invalidate your card without formally canceling, they treat it as ever-increasing unpaid debt and eventually send you to collections, and then you've entered the hell world of aggressive debt collectors and potential damage to your credit.