In a totalitarian or authoritarian dictatorship, government officials do not need the support of the citizenry to exterminate freedom of speech. That’s because there are no elections to worry about. The regime simply starts having its military and paramilitary goons start arresting critics, disappearing them in terrorist confinement facilities, torturing them, and then killing them. Everyone else understands. No more criticism of the regime.
In a democratic system, suppressing criticism is much more difficult owing to the problem of elections. If the goons of some democratically elected president begin rounding up critics, incarcerating them, torturing them, and killing them, the ruler runs the risk of being kicked out of office in the next election. There is also the risk of impeachment.