Why hotdogs aren't considered sandwiches

To qualify as "a sandwich," a given food product must, structurally, consist of two (2) exterior pieces that are either separate or mostly separate;

Those pieces must be primarily carbohydrate-based-so, made of bread or bread-like products;

The whole assemblage must have a primarily horizontal orientation (so, sitting flush with a plate rather than perpendicular to it); and

The whole assemblage must be fundamentally portable.

So. Under this definition, a burger is a sandwich. So is an ice cream sandwich. So is an Oreo. So is a grilled cheese. But not a hot dog