This is a classic case of the just world fallacy.
Historically, representative democracy with one man one vote exists because that was the result of the last compromise between the underclasses and elites trying to keep them from getting out of hand.
It isn't any more theoretically reasonable than the compromise before that (no women voting), or the one before that (no blacks) or the one before that (nobody votes who doesn't own property) or the one before that (nobody votes).
Who is experiencing the bias here, the founders of the representative democracy or me for pointing to the political theory? I assume you're talking about some system that isn't the US government, because otherwise your recollection of history is way off.
"Theoretically", we had kings because of the divine right of kings. Theoretically the American expansion was justified by manifest destiny. Theoretically women were not allowed to vote because "90% did not want it" or because it would "place the government under petticoat rule".
Theoretically, today, we have representatives in government because the people aren't smart enough to represent themselves.
Every system of power and domination creates a justification for its own existence and it's nearly always bullshit.
You might want to reserve the use of the word "fallacy" for cases where an argument's logic does not follow. Ironically, use the word otherwise often betrays one's own cognitive biases.
As far as my endorsement, I don't think I could state my position any more clearly than I already have: "...maybe we should reconsider the wisdom in granting some small portion of our freedom to every other voter. 42% of Americans believe in ghosts..."
You have yet to make an argument that "representatives are theoretically there to guard against majority tyranny." If you had, it wouldn't be a just world fallacy.
Correct, I have no interest in arguing that position. Any highschool graduate should immediately recognize "majority tyranny" and the political theory that it is connected to. If I had argued the virtue of representative democracy, it might have been biased by the just world fallacy, but I haven't - so it wasn't.
Also, Switzerland does not vote on every law with a referendum.
The question is whether democracy needs bureaucracy, and if so, how much.
Obviously, democracy requires certain decisions to be made according to certain processes, which take time.
So you can't do away with all bureaucracy.
The documents aren't going to push themselves. :)