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?

The usual non-prescriptive example is Platonic ideals.

https://en.wikipedia.org/wiki/Platonic_idealism