Even in the relatively recent founding history of the United States, the Federalist Papers discuss and try to address a variety of issues which can lead to this outcome.

And ultimately, I think this is what we see with the Brexit outcome and the current Trump campaign in the US. These aren't "new" concepts...throughout history we can see similar outcomes for similar events with similar reasons.

You raise an excellent point though, which is with the ease of communication in the modern era, why don't we have a more informed public? This is something I have thought about trying to tackle with a side dev project...but the issue is complex and difficult to address directly.

Side note, I believe the Roman Empire was a Republic, not a Direct Democracy :)