Giving the impression they have a relationship with the restaurant is exactly why it's damaging the restaurant's reputation. The distinction you make doesn't exist.
The act of sending a dasher to a business they don't have an explicit relationship to deliver their food -- totally fine. The app not making it clear that the restaurant isn't partnered with DoorDash and that they're placing a pick-up order and delivering it to you -- not fine.
Making "damaging the restaurant's reputation" a thing is absurd in all aspects. By the restaurant owner's own logic picking up my own order without an insulated bad shouldn't be allowed -- after all what if I get home and the pizza isn't as good because it's cold? That could hurt their business. Utter nonsense. Do we now have to decide whether "it's fair" that something potentially hurts their reputation? Is a bad review fair if it's about the food, but unfair if it's about the wait?
What DD did is bad because they impersonated the other business, not because people got soggy fries. You stop getting to curate the dining experience the moment they walk out your door.
