Why didn't Makishima spread the video of the Sibyl system?
People would have gone so crazy about this (if it wouldn't be immediately "debunked" as fake by Sybil), and then everybody would be targets for execution or imprisonment.

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.