And so I think the methodology is (sort of) prescriptive: whatever you do, if it isn't equivalent to a linear combination of your subvalues, then your aggregation procedure is introducing new subvalues, which is probably a bug.

I tried to argue against this in the top level comment of this thread, but may not have been very clear. I just came up with a new argument, and would be interested to know whether it makes more sense to you.