basically it would upset the muggles. look at the responses here: all of them are based on vacuous analogies to ancient systems, dredge up irrelevant issues like voter intimidation, or praise politicians (who would certainly still exist, as would parties) or that less indirect democracy would somehow eliminate the constitution. or worse: suggest that voting security would be a problem.
the main issue is that muggles are used to the dysfunctional system we have now, and the vested interests are comfortable with how they can keep things under control. or to put it another way: the voters who are unhappy with the current system are getting some catharsis through Bernie and Trump, and the latter group will probably spend their load well before the election.