I find that system inconvenient, as it does not inform me of how I should eat any given item. Classification for the purpose of classification is insufficient. However, an alternative that allows me to prepare my ustensils based on the classification is useful, and therefore I propose…
Soup, salad, and sandwich are the three states of food, and they can go through phase transitions. They are closely accompanied by spoon, fork, and knife, respectively.
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A soup is any food that requires a spoon, and thus includes soups, drinks, cereal with milk, etc. Tipping a container is merely the use of the container as a large and unwieldy spoon, a straw is similarly a spoon when its topology is combined with suction.
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A salad then is anything bite sized that can be forked, and one’s hands are little more than fleshy forks, the fingers prehensile tines. Popcorn, salads, cut up steak bites, a handful of cheerios, etc.
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A sandwich is anything that requires it to be cut in order to be consumed, and one’s incisors are merely built-in knives. A sandwich is thus the vast majority of the cube rule’s content, and only because the cube rule focuses on the physical location of the starch. This is, of course, entirely irrelevant when it comes to the consumption of food.
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To observe a phase transition, one can cut up a sandwich without consuming it, thereby turning it into a salad; can drown a salad to turn it into a soup; can freeze a soup to turn it into a sandwich, etc.
Shredded cheese is a salad.
I mostly agree with these broad level classifications, except for sandwich. A sandwich refers to the construction (something sandwiched between something else) and also the intended method of consumption (no utensils and rarely a napkin). By your classification a 32oz steak is a sandwich, yet it must be consumed quite differently than an ice cream sandwich.
I’d change the sandwich category to be the chunk category, and have sandwiches as a subcategory of chunks and salads where the food comes surrounded by edible material that’s easy to handle without utensils.
There’s also the group of very thin soups that might deserve it’s own group, but that might just be a qualitive difference.
While I think your system allows for some really odd edge cases, I like the way you think.