In episode 17 Makishima is handed Gu-sung Choe's phone with a video that shows the the Sibyl system's true form.
An episode earlier Gu-sung Choe said that if this video were to go public it would be the end of the country.
After Makishima escaped the aircraft he could have uploaded this, why didn't he? It would have been much easier instead of trying to poison all food supplies.
People would have gone so crazy about this (if it wouldn't be immediately "debunked" as fake by Sibyl), and then everybody would be targets for execution or imprisonment due to a sharp rise in crime coefficients.
Or it would not do anything at all. Remember how people sometimes would decide on their own that something that looks horribly wrong can't be real, because otherwise the above would happen, and so they just go on along, like it's a prank or something that doesn't deserve a second thought.
So the more effective way of thinking would not be a risky revolution attempt like this, but a behind-the-scenes action that would definitely do something, without relying on people's thoughts.
I think this has also been answered in the anime indirectly when Touma Kouzaburou offers Makishima to become part of the SiByl system, the answer given by Makishima is more or less that he does not want to become an almighty but continue to be a player, if you think about fun then of course it will be boring to end it in the way that was mentioned earlier.
If I remember correctly, the underground levels where the Sibyl System is installed are completely isolated from the outside world, so the video most likely couldn't be uploaded, and the device in which it was stored was probably destroyed by Sibyl.
