I don't think Papa John's keeps a history of addresses on every account but even if they do, it would be useless because if someone enters their account and sees that their free pizza is gone they would have to file a police report and get a warrant from a court to gain access to this history of addresses and nobody does that for one pizza or even ten pizzas. It would cost them a lot, nobody would take them serious and it would take them months to do that.
The only reason deleting the address is a good idea is because that way you won't get angry people knocking at your door and demanding you to pay for their pizzas
The point is, it is safe to use those accounts even with delivery, but if you want to be extra cautious you can always use pick-up.