... There are other means for the elite ($) to have the last word...(etc)
Actually, the whole point of a Republic is to put speed bumps into what would otherwise be a pure majoritarian process by setting up a careful balance between involved entities.
In case you haven't noticed, purely majoritarian processess tend to degenerate fairly quickly, as people's Rights and limited governmental Powers tend to become whatever 50% +1 person say they are. If 50%+1 say it's your right to wear funny hats, and a governmental Power to ensure that everyone wears their funny hat, it becomes funny hat time pretty quickly.
The original balance was not struck between the "3 branches", it was actually struck against 5:
-The executive
-The judicial
-The congressional
-The States
-The people.
Essentially, the states had the power to appoint the executive, senate and executive officers, via means of their own choosing. Also, they originally had functional control of the pursestrings as well. (He who has the gold makes the rules....)
For all practical purposes, the States have been written out of the balance, now holding only a ceremonial role in the appointment of the executive via the electoral college, having been stripped of their powers otherwise.
As a result, the overall balance of power and money has shifted away from the more local level of the states, where presumably a citizen could have more influence, and is now distantly centered at the fedgov, and this is a source of a great many of our current problems. Pork barrel politics wouldn't have nearly the allure they do now if there was less pork to fight over, and politicians wouldn't be obliged to scramble with each other over getting what they consider to be their fair portion of their citizens money BACK.