To be "democratically elected" means that the people "en masse" directly decide what the rules of each election will be, as well as who is to be elected, and when. Once you do that you wind up with chaos - mob rule.
No one elected under these circumstances can truly be "representative" of the people since the people (the mob) can reelect another "representative" at their whim.
That's certainly what the Founders had in mind when they made this a Republic - not a Democracy.
Not necessarily, the people do nominate and elect their representatives "en masse", but they do so under existing election laws and predetermined proceedure enacted by their elected representatives. Pure democracy would be a referendum on every single issue. If you take the "democratically elected" out of the equation, you would have a representative rebublic installed by only a certain portion of the population, say land owners for example. Our present sytem has aspects of both pure Republicanism and pure Democracy.