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First, an understanding: The justice system doesn't exist for the benefit of the general public, but for the benefit of those specific members of the public accused of crimes.  We're very good at vigilantism, not necessarily good at vigilante -justice-, and from what I have personally seen, 90% of what police do is discourage vigilantism; I think the death penalty results in fewer vigilante killings than it involves in executions, particularly in states like Texas.

Understanding that the justice system doesn't exist to protect the unaccused innocent, but rather the accused innocent, a lot of what goes on makes a lot more sense.  How many people have you encountered who "Just needed killing?"  Whose sole claim to life is that a penalty exists for taking theirs?