To me, this misses the point of the Justice System. The function of the Justice System is to allow people to live together by administering, fairly, a set of rules that all know and have, by remaining in the country when they know the laws, agreed to abide by. Prosecution and punishment are a means to that end, not an end in themselves. If we have rules, we need to punish rule breakers. But if we have punishments, we need to reassure people that the law abiding will not be punished: and the mechanism for doing that open trial with guild established beyond reasonable doubt.
So it is more important that justice is seen to be done than it is done. The "beyond reasonable doubt" rule establishes this. Of course, the easiest way for justice to be seen do be done is for it to be done, where it can be seen. And secret trials break this paradigm. It will not deter other plotters from future plots, because they don't know about it. It might take two dangerous men off the streets - but can that not be done other ways, with a simpler and mor publishable level of proof?