To me, it sounds more like an argument against listening to the loudest voices. So our (UK-perspective) elections go some of the way to achieving a well-functioning democracy, since the literal act of voting is egalitarian. The issues surrounding how those votes are influenced by the loudest voices, however, still have to be resolved.

Not necessarily. You can have proportional votes for representatives and then let those representatives make decisions that don’t reflect majority opinions when e.g. those decisions protect minorities.

Quite a lot of the classics were written by hereditary dictators and aristocrats, members of tiny elites so the anti-democracy angle is incredibly common.