As is most often the case, it is simply a matter of just being an established convention.
IDIOM if you like. And idiom is by definition non-explicit. Also prepositions e.g. *durch*
or *through* are inconsistently used in different languages "den ganzen Tag über",
(*through the day*).

Now while *durch* seems to suggest a flow of stuff between recipients, *geteilt auf* might have, by an accident of history, become the most fitting idiom for the act of arithmetical division.