The essence of a representative republic is that these horrible leaders would still be checked by the minority of non-horrible leaders. In a direct democracy,

The essence of a representative republic is that these horrible leaders would still be checked by the minority of non-horrible leaders. In a direct democracy, the mob only needs 51% of the referendum. In representative government, a minority of representatives can prevent disastrous legislation from happening, through the threat of filibuster or by holding a more valuable (to the opposition) bill hostage. In 2009 when Democrats held a Congressional majority, they didn't get everything they wanted. Now in 2015, Republicans hold a Congressional majority, they still don't get everything they wanted. Whichever side you're on, you must admit that these checks prevented the "bad guys" from prevailing.