By voting through feel-good proposals that are ultimately misinformed and destructive. It’s happening anyway through our indirect democracy but at a slower rate.
I would guess the Swiss population is generally more educated on average compared to the American public, which to be fair is easier to achieve with a population of 9M vs 328M. A sufficiently educated public is a requirement for a more direct democracy to have desirable results.
America really needs an education system overhaul, teachers are often paid close to fast food restaurant staff levels of wages.