"So-and-so for president" is simply the traditional way to do this. We have a set usage of "elect s.o. for position title", where position title is the title of the job, with the meaning you are intending. It is not some other description of the position, simply because that is not how the phrase is traditionally constructed. There aren't syntactic or morphological rules that force this to be the case -- it is decided on semantic/pragmatic grounds.
We do the same for any type of position (items with preceding question mark = awkward at best):
- John for mayor / ?mayorship
- ("and the Emmy goes to...") John for best actor / ?best acting
- John for father-of-the-year / ?fatherhood-of-the-year