A pure democracy would be one person one vote on ALL matters. It simply would not work on a large scale. That is why No actual Government anywhere is a pure Democracy.
historically you are correct but now with the power of the internet REPRESENTATIVES are NO LONGER NECESSARY i.e. everyone COULD vote their own opinion on any and all govt. issues...that begs the real question do we really WANT to allow each citizen to vote on any/all issues? In a REAL DEMOCRACY that would be required but there is a good argument to be made about not allowing morons to vote
In our Republic, the Federal Government is a congregation of Sovereign States. That is why Represetatives represent particular constituancies and why the individual states send particular delgations to the Electoral College to elect the president.
The Senate requires a 60% majority to pass anything and this, according to Jefferson, prevents the "tyranny of the majority".
Our Republic was constructed to preseve and represent the unique identities of the several areas and cultures of the country.
Your idea could result in all of the "Representatives" living in one area and a defacto oligarchy.
In terms of governmental types, a lynch mob is the purest representation of democracy.