Democracy gets traded for dictatorship because someone shows up and says "I might not be perfect but I'm a hell of a lot better than these schmucks who've been ruining things". And when that person saying that stuff shows up at a point in time when the people who have been in charge of things have run the country into the ground with wars, debts and policies that give people no hope that things will get better, it's a pretty compelling message.
It would be, if it were true. But the premise isn't true and the solution isn't true either. It just sounds good and people tend to respond from fear and other emotions rather than rationality.