!
Exactly. Hot dogs are ubiquitous and yet unique enough, that we don't need to place them into a broader category. Pretty much everyone knows what a hot dog consists of. There may be different ways of preparing a hot dog; some may be longer than others, some may have a ludicrous amount of condiments and toppings, the social acceptability of specific condiments may vary from place to place (regional differences between hot dogs in New York and Chicago are a classic example); but those would be different varieties of hot dogs.
Trying to tell someone a hot dog is a sandwich only serves to introduce confusion to a generally, well understood food. If you order a wiener or frankfurter sandwich, don't be surprised if they don't know what the hell you are talking about.
Clearly understood language is a wonderful thing, let's not ruin that by trying to add confusion to it.
Let's instead just call it a hot dog, and leave future historians to figure out what it is later, it will be funny.