What if you no longer have an account at the issuing bank and the cards were cancelled. How would this even work given there is no business relationship anymore?
It only works if you have an active account with the issuer. It's simply a convenience feature for subscriptions to go to the new card since it would be rather annoying to have to go through 20 different subscriptions to add the new card.
That's fine. Most people don't want to have to re-enter their new credit card everywhere, so you can always call your issuer and ask them to issue a new card, but stop all subscription charges.