It’s definitely pie, because the entirety of it’s carbohydrate layer is called crust. Both pie and bread have crust. But in bread, crust is the layer that’s browned and hardened in maillard reactions. It stands in contrast to the crumb. In pie, the crust is the entire outer carbohydrate portion of the dish, defined in contrast to the filling. Nobody refers to a pizza’s crumb (the airy, non-maillarded portion of a bread). The entirety of the carbohydrate base is deemed crust. Therefore, pizza is a pie.
But pizzas do not having fillings. They have toppings instead. And what of pizzas that have sauce and toppings right to the edge of the crust? Are they hot open-face sandwiches? Italians fold the slices which might suggest they are tacos. Overall, they more fit a flat bread with these things in mind.
Pies take various forms. There’s no rule against covering the crust.
Sandwiches and flatbreads have bread as an ingredient. You don’t bake sandwich slices in the oven around a ham and cheese. A flatbread is made by piling toppings on an already baked bread. A tomato sauce, mozzarella and pepperoni flatbread is distinctly different than a pepperoni pizza, no?
I could go on and on. There are many reasons pizza is a pie and bread-derived foods are not.
Now, is a calzone a sandwich? Still no. More like a hand pie.
What if the top layer was cheese, and the other ingredients were placed between the crust and cheese layer? The sauce/meat/vegetables would then be considered a filling.
Depth again.