The problem with direct democracy is that the modern world is very complex and most people have zero idea about matters of importance. Most people have beliefs they’ve never bothered to verify, ideas that are profoundly in error, and form preferences based on irrelevant criteria. It’s not difficult to imagine the consequences of direct democracy in which everyone above a certain age threshold is permitted to vote. Furthermore, who proposes the legislation being voted upon? As it’s so easy to manipulate people (think the Brexit lies) it’s easy to see that whoever frames the ballot gets to control the outcome.
Until we accept the need for demonstrated competence before individuals are permitted (i) to propose legislation, and then (ii) vote for/against it, we’ll continue to see stupid people clamoring for stupid things. Populism isn’t the result of dissatisfaction with representative democracy; it’s the consequence of a world in which everyone believes they are competent to have opinions on matters about which they are profoundly ignorant and so are easily led by the nose by blustering charlatans.