That is an ahistorical assumption. The wish to silence, censor, and impede thought is just as strong a human emotion as the desire for free expression -- especially when censorship is cloaked in rhetoric about fairness, equality, justice, and all the other euphemisms for not allowing the free promulgation of ideas.
George Orwell devoted his later years to warning us that while the fascist method of destroying free expression was easily identified (albeit only with difficulty combatted), the leftwing totalitarian impulse to squelch unpopular speech was far harder to resist -- couched as it was in sloganeering about the "people" and "social justice." It is easy to object to the speech codes of a self-interested, corrupt dictator in sunglasses and epaulettes, but difficult to fight censorship that allegedly helps the poor, minorities, and the helpless.