Severian's Argument: The Laws Are the Laws

There's absolutely no question at all of the guilt of this guy, right? Like he did something horrific in the vision of hundreds of people. He also used a unique weapon. The evidence of someone dying by auburn bite is probably pretty clear compared to like a sword or a mace or something like that. This is really clear. We shouldn't need this Byzantine process in the middle of it. Let's just kill him, right? Why can't we expedite the process and actually execute the laws quickly?