Well, if the customer with the expired payment information is still using and valuing the service, he will soon realize that he needs to update his payment information without any outside intervention or he will lose access to the service. If the user no longer cares about the service and just forgot to cancel or was to lazy to do so, why not just let him go instead of continuing to sell him something he does no longer need?
UPDATE: I probably got the wrong first impression - I thought the service was kind of last resort if the user did not respond to the normal notifications that he will lose his service; I missed that you can completely outsource this.
UPDATE: I probably got the wrong first impression - I thought the service was kind of last resort if the user did not respond to the normal notifications that he will lose his service; I missed that you can completely outsource this.