I am fairly certain I can split an empty pile into two empty piles, without a remainder.
;-)
But a plate is its own thing, in addition to what goes on it. A "full plate" is full of what? And a full plate is the plate plus whatever is on it, not just the stuff on it.
I think of a "pile" of stuff as being it's own thing, that being the pile itself. An empty pile is the absence of the thing.
That was my interpretation, but I see what you meant. :)
At least this would explain their reasoning in terms I can understand.