Then when grandma comes to visit, she gets a parking ticket because she didn't get the right permit?

No, the better option is for shopping centers to have enough parking for the customers they anticipate having. Maybe giant parking lots suck, but a business shouldn't be able to destroy a residential neighborhood like that.

I've lived in plenty of places where the stores were above the parking garages, and no one from the street could tell there was any parking at all. That's always an option.