What is it that makes a PB&J clearly a sandwich, and excludes a stack of pancakes with butter in between - and doesn’t exclude a club sandwich.
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.
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.
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.
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?
Regardless of these facts and it not meeting your criteria, it is still both in common usage and by explicit name a sandwich!
(Also, love it!)
(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.