@SophieLibkind : I think you are considering a different theory, i.e., one based on a different preorder: John would not write "lemon ≤ lemon filling", but "lemon+butter+sugar+yolk ≤ lemon filling" (unless he decided to abstract from the need of the latter three ingredients in the same way as he is abstracting from the need of using a bowl and other tools).

I suspect that the reason for preferring a theory where "≤" is used for giving information on the resources that are sufficient for the output is more manageable than one in which it is used to give information on merely necessary resources is that it "composes better": if we wrote "lemon+butter ≤ lemon filling", "sugar+yolk ≤ lemon filling", and had one dose each of lemon, butter, sugar and yolk, the formalism would not be able to tell us that we get exactly one dose of lemon filling, rather than two or an undetermined number.