Because it yields a situation which the largest number of people is OK with. It maximizes the satisfaction of the people with the legal system.
> We don't hold referendums on every other issue.
We not doing something does not mean that we shouldnt. We absolutely should have more referendums.
> I'm not sure you'd like a world where politics was entirely reduced to the lowest common denominator
I'm sure I dont want to live in a world where laws directed against the population can be purchased by a few uberrich stake holders, where laws binding for everyone can be decided behind closed doors, without any legal way (other than useless protesting, campaigning, begging, etc) for the population way to get rid of unjust, bad laws and corrupt politicians.