Your 2nd point is why it can’t be. Opens up Pandora’s box in the sandwich world. Sandwiches will be claiming pizza and calzones eventuallyIt has bread with stuff inside of it, so yes
A more controversial question would be whether a taco or burrito is a sandwich or not
I feel dirty saying this, but I think a calzone is arguably a sandwich too. I'll definitively draw the line at pizza though. That isn't a sandwichYour 2nd point is why it can’t be. Opens up Pandora’s box in the sandwich world. Sandwiches will be claiming pizza and calzones eventually