The Athenians had real problems with direct democracy. Plato is still relevant:
Plato rejected Athenian democracy on the basis that such democracies were anarchic societies without internal unity, that they followed citizens' impulses rather than pursuing the common good, that democracies are unable to allow a sufficient number of their citizens to have their voices heard, and that such democracies were typically run by fools. Plato attacked Athenian democracies for mistaking anarchy for freedom. The lack of coherent unity in Athenian democracy made Plato conclude that such democracies were a mere collection of individuals occupying a common space rather than a form of political organization.
Corporations don't need to buy off half the people, they just need to convince a winning minority to go along, which you've made easy because you've divided all of your political issues into things people pick and chose not out of expertise but out of ignorance. There are other issues like control of the agenda which aren't obvious but hugely relevant to controlling democracies.
Was Prop 8 in Cali, with lots of outsiders weighing in on limiting other people's rights a good thing?
This is my macabre favorite story about Athenian democracy:
The news of the victory itself was met with jubilation at Athens. Their joy was tempered, however, by the aftermath of the battle, in which a storm prevented the ships assigned to rescue the survivors of the 25 disabled or sunken Athenian triremes from performing their duties, and a great number of sailors drowned. A fury erupted at Athens when the public learned of this, and after a bitter struggle in the assembly six of the eight generals who had commanded the fleet were tried as a group and executed.
Sucked for those generals. Win the battle, lost men due to storms, then you get executed because the mob is angry and some orators know how to harness that. Modern direct democracy wouldn't be voting on executing people, but you can see where things can get just as twisted.
https://en.wikipedia.org/wiki/Battle_of_Arginusae
spoiler: the Athenians lost the war. Turns out getting rid of winning generals cause you're mad is dumb.