It breaks down with edge cases. There are a few documented "ring species" such as a diverse land-based amphibian around a lake. At all points the adjacent neighbours can mate, but if you take examples from the far side of the lake, they cannot. One species? Two? Infinite?
I think it was Richard Dawkins who extended this idea through time. We could mate (sorry) with our immediate ancestors, who could with theirs, etc. and in fact there's a continual chain like that all the way to any other mammal. When did we stop being our ancestral species and become H. Sapiens? No clear line.
A ring species is an example of a species complex, and subpopulations with different but not mutually exclusive breeding compatibility are known as microspecies. If populations with distinct morphological features are isolated in space or time but could still interbreed with eachother if they were to be brought into contact, they are subspecies.
This is really just an instance of Sorites paradox. But the inability to draw a precise line between two (or more) states does not mean there aren't two (or more) states.
If you eat two pancakes with butter between like a sandwich, it is a variant of butter sandwich. If you cut up your PB&J such that you're only eating pieces of bread with some spread on them, that is not a sandwich. The bread must act as a container for the contents during consumption, regardless of ingredients.
More generally, the key delimiter for sandwiches is the aspect ratio of the individual items contained by the bread. For something to be a sandwich, all of the major items inside must have one dimension which is substantially smaller than the other two. Sliced meats, bacon strips, cheese slices, sliced vegetables, lettuce leafs, spreads, patties, etc are all valid. Thinly spread peanut butter and jelly between bread is a sandwich, but a bread bowl with a pool of jelly and peanut butter where the depth is comparable to the radius would not be a PB&J sandwich. Flat cheese slice between bread is a sandwich, mozzarella sticks are not sandwiches. Hot dogs are by default not a sandwich, but if you cut the hot dog into thin strips it becomes a sandwich. An oreo is a sandwich but a quadruple stuffed oreo is not. The only commonly accepted sandwich which this definition claims to be a pseudosandwich is the meatball sub.
You're carving out a definition to fit intuitive inferences gleaned by observing instances of "sandwich" and "not-sanwich" labeled by influential people in your life who had no objective reasons for constructing and perpetuating those categories in the first place.
I agree it would have been a lot easier if we precisely defined the sandwich before foods were invented so we'd know which category to place them in ahead of time, but alas barring the invention of time travel we have to deal with our forefathers' mistakes.
But what about the named club sandwich, which 1) has a width to height ratio so unfavorable it needs toothpicks to hold it together, and 2) often has more bread than ingredients (at sub-par establishments), but sometimes far more ingredients than bread (leveraging the toothpicks).
Regardless of these facts and it not meeting your criteria, it is still both in common usage and by explicit name a sandwich!
It's not the thickness of the sandwich, it's the thickness of the individual things in the sandwich. Everything in a club sandwich is flat, there's just a lot of stuff.
(Sorry, can't resist keeping this going, this is some good discussion).
It's true I guess that the aspect ratio for most ingredients is 'flat', but many are thicker than the bread, and the whole sandwich is 'sideways' aspect ratio wise.
This definition includes open faced sandwiches so long as their contents have the appropriate aspect ratio and you hold them via the bread. If you needed two pieces of bread to make a sandwich then that would rule out everything served on a roll. Pizza is an open faced true sandwich, pancakes are not.
That said, just because something has a word in the name doesn't mean it's a subset of that category. Strawberries aren't berries, english muffins aren't muffins, prairie oysters aren't oysters, black pudding isn't pudding, etc.
The aspect ratio rule fails for a bagel-with-cream-cheese from a NY food cart, clearly a sandwich, which has a square of cream cheese which is as large as the bagel in 2 of 3 dimensions.
I don't really get how your prescriptive rule means open faced sandwiches somehow "contain" their contents. Then again, since I don't believe in being prescriptive, I don't really care to think hard enough about the contortions of logic required by your approach.
But it has 1 dimension, it's thickness, which is substantially smaller. You don't have a cube of cream cheese, you have a thin square. Thus it satisfies the aspect ratio rule, which, again, says there is one substantially smaller dimension than the other two.
A container is something which contains. If you can manipulate something by the bread part and the contents stay put, they are contained. While the aspect ratio rule may be legitimately controversial, if you don't restrict your definition of sandwich at least to stuff contained by bread then what isn't a sandwich?
The whole point of this exercise is to taxonomically categorize foods as being sandwiches or not sandwiches, how would you do that without being prescriptive?
I think it was Richard Dawkins who extended this idea through time. We could mate (sorry) with our immediate ancestors, who could with theirs, etc. and in fact there's a continual chain like that all the way to any other mammal. When did we stop being our ancestral species and become H. Sapiens? No clear line.