While you are right, terrorism is a threat to humanity, I"d argue one can more easily prevent terrorism by keeping the terrorists alive. This helps in a number of ways, for example, we can get information from them. Maybe we could even reform them to help us(most likely though the media, which would raise western spirits and make the terrorist organisations somewhat sad).
You should rethink, think about all the potential evidence and their plots to murder from a captured terrorist. This could save so many lives because of our knowledge.