I haven't heard "usage of censorship." "Rationale for censorship" sounds fine to me. I am curious about what you are trying to say, though.

The phrase "usage of censorship" is certainly possible. For example: "The government of Country X has been frequently criticized over its brutality and usage of censorship." That is a perfectly correct sentence. (However, most people would use the more common word "use" instead of "usage," without any change of meaning.)

A similar word to "rationale" could be "justification." For example, you could say that a country at war has a justification for censorship to prevent the enemy from learning of its military plans. I agree with Eliot that "usage" is not the right word here.