This could easily be an option in the edit payment system and it's not. This raises the question why does Adobe intentionally store data such as credit card numbers, names, and addresses of its customers against their will unless they jump through hoops to get it removed. I think this choice is likely rooted in greed and perhaps to take advantage of less organized or less tech savy customers who may not know to cancel plans before the renewal date if they don't want to be charged. Adding a delete button to the edit payment system would provide customers with a better service that they feel they can trust with their information and free up the customer service reps that would no longer have to get them removed on the back end, but I don't know maybe Adobe isn't capable of making functional UI.
You could hardly cancel the payment without cancelling the plan - that would leave you unable to fulfil your site of the agreement. Adobe should allow you to CHANGE the payment to a different card. You seem to suggest that removing payment would make a contract go away, but this would just leave customers with ever increasing debt! A very bad idea. It would be good, however, if there was a button under the payment which led the customer to the option of cancelling the plan, settling any cancellation fee, and removing the card all in one.