A large portion of our society isn't just ignorant, they celebrate their ignorance. We elect officials, who are (hopefully) better educated than the average citizen. We hope they make the best decisions for us. Though, many are cynical & believe that a lot of back room stuff is for them to make the best decisions for the elected politicians. And, though this doesn't happen always, it certainly does happen (see gerrymandering for one obvious example.)
With direct democracy, it would be a clusterfuck. Let's just talk about tax rates - there's been plenty of discussion about tax rates for the rich lately. I think it's safe to say that the majority of Americans don't even understand marginal tax brackets - the number of people who think that if you earn x number of dollars, then you pay one percentage of your income, and magically, if you earn x+1 number of dollars, then you pay at a different rate. Even educated people posting on this forum have inadvertently pointed out that that's what they had thought. It's an incredibly common belief - I hear people discussing it all the time at various companies: "It's not worth it to work overtime, because they take so much more out in taxes." And, you want THESE people having a significant say in tax policy??