Someone needs to go out on the streets and ask people to describe pizza. How many average joes out there are going to say "200 gram balls of dough covered with 80 grams of san marzanos, covered with 100 grams of fresh mozzarella." I think most of them will say something along the lines "dough sauce and cheese."
What I mean is, I think the general description you would get of pizza from the general public would apply to chicago deep dish as well as it would apply to NY, Neapolitan or sicilian pizza.
Maybe we should call all pizza by it's true name "open face calzone"