Earlier quoted context omitted.
First of all, a pie must be baked, so that would eliminate omelettes, pancakes, and more from your list. Second, a pie must have a crust and a filling. That eliminates a lot of the list too. Second, a pie needn't have pastry on both top and bottom. There are numerous pies with no crust on top, such as pumpkin pie, key lime pie, banana cream pie, lemon meringue pie, chess pie, pecan pie, or chocolate icebox pie. These…
Interesting view regarding the pastry on top. Would you consider https://en.wikipedia.org/wiki/Lasagne , https://en.wikipedia.org/wiki/Moussaka , and other https://en.wikipedia.org/wiki/List_of_casserole_dishes all pies then? Toasted sandwiches are baked and by your definition could still then be pie . If you would argue otherwise, where do you draw the line between baking and toasting?
I wouldn't consider a toasted sandwich to have a crust because to me a crust is more of a hard pastry layer, not a fluffy piece of bread which has been browned.
Though that is a bit of a gray area. If you were to take some fluffy white bread, get it wet, and mash it down into a layer that lines a pie pan, and then put some filling (fruit for example) in it and bake it, and if the bread all hardened together into a cohesive outer shell, then I suppose I'd call that a very unconventional pie.
Just to make everything more complicated, there are deep-dish pizzas that have a very pie-like form. There's crust on top and the bottom, and they are cooked in a pan that resembles a pie pan. For example, this: http://winespiritsbeer.blogspot.com/2013/09/beer-crust-deep-... . Compared to a flat pizza, I think those are more deserving of the word "pie" not only because there is a crust but because the ingredients are more of a filling and less of a topping.
Another question is whether a (baked) calzone or empanada is a pie. They certainly meet most of my criteria, so maybe I'd have to say they are.