Is a hotdog a sandwich?

Hotdogs have been sandwiches since their inception

Question: Is a hotdog a sandwich?
Position1 of 2›: Yes, a hotdog is a sandwich
Argument‹2 of 2: Hotdogs have been sandwiches since their inception

In the US, hotdogs were first referred to as sandwiches. Since then, the hotdog has become a quintessential part of American food culture and its status as a sandwich must reflect that.

The argument

The argument here is about classification rather than taste, and it looks to the point of origin. Hot dogs were first introduced to America in the 1800s, at Coney Island in New York, and among the first nicknames attached to them were "Coney Island Sandwiches" and "Frankfurter Sandwiches." On this view those names are not incidental. A name given at the moment a food is introduced records how the people who introduced it, sold it, and ate it understood what they were handling, and what they understood themselves to be handling was a sandwich. Proponents accept a limit on the claim. The Germans, as the original creators of the food item, may never have thought of it in those terms, so the argument is not that the hot dog is a sandwich everywhere and from the beginning of its existence. It is that in America, where the present dispute is actually conducted, the thing entered the language already classified, and it entered it as a sandwich. The remaining step concerns what would justify reclassifying it. Food categories are conventional, and conventions can be revised, but a revision needs a reason: some change in the item itself, or a defect in how it was originally sorted. Neither is on offer here. What has changed is only that many people now find the label counterintuitive and hold that intuition firmly. Stubbornness of opinion, on this account, is not an argument for recategorising a product; it is the absence of one. Since the hot dog was called a sandwich in its original glory days, and nothing about the hot dog has altered since, it must still fall under the category it was placed in from the start.

Premises

[P1]When hot dogs were introduced to America at Coney Island in the 1800s, they were nicknamed "Coney Island Sandwiches" and "Frankfurter Sandwiches." [P2] The food was therefore classified as a sandwich from its earliest American days. [P3] It makes no sense to change a product's original categorization simply because opinions later became stubborn. [C] Therefore, because hotdogs have been sandwiches since their inception, a hotdog is a sandwich.

Counter-arguments

As mentioned, the hot dog is not considered a sandwich EVERYWHERE. If it's not a universal thing, why should every single hot dog be categorized as a hot dog? I f everyone can't agree on it, why place a controversial label upon it?

Rejecting the premises

[Rejecting P1] Early nicknames record how an unfamiliar food was sold to American customers, not a settled classification; they sat alongside other names for the same item. [Rejecting P2] A nickname is not a taxonomy. That vendors called it a sandwich no more establishes the category than "hot dog" establishes what it is made of. [Rejecting P3] Ordinary-language categories are fixed by current usage, not by first usage, and the argument gives no reason why the earliest label should bind later speakers — particularly when, as the counter-argument notes, usage is not uniform even now.