If you're wrong about that, we'll win the War on Islamo-fascism by continuing to silence martyrs.
Very simplistic answer.
What you call "martyrs" are merely foot soldiers.
If you are going to kill somebody, it is far more effective to kill the radical cleric than poisons a thousand young minds or prove him a fool to his followers than to wait ten years to kill the product of such a poison.
The poison has already been unleashed by this man's arguments and future generations will see that your response was neither to kill him nor prove him wrong but to merely prohibit even bringing up the subject.
To put it less simplistically, most people recognize and reject epistemological relativism. Most people know the difference between an Islamo-fascist and an average American who would not want our nation to become a theocracy.
So a violent, Islamo-fascist propagandist will gather a few abnormal, unhealthy followers within a given amount of time. Give him more time, and he'll gather more losers. Give him enough time, and he might gather enough to perpetrate much violence. But if we shut him away from being able to propagandize to others and humiliate him, he won't be able to gather more prideful followers.
Liars don't need martyrs. Because if they set out to propagandize murder of whole ethnic groups, the same liars tend to fabricate histories of martyrs. Regardless of (and partly because of) their tactics, we win wars against them. Perpetrators of the big lie tend to be vain--blind to the fact that most educated others see them for what they are.