By that reasoning, sure, it is not arbitrary, it might be the most efficient way to resolve things without complicating the notation we have to use. The point about it being arbitrary was more to say that there is no real mathematic basis for it, we have simply agreed to do it this way so everyone applyingnit arrives at the same “correct” solution.

Arguably it has little value in algebra too, since it tends to be written less ambiguously, tho I have not had to really use algebra much since highschool (weirdly it was not a huge part of medschool, at least here, occasional use in chem and phys only).