How do you judge what constitutes a criminal that is just "trash?"
According to you, someone who robs or steals deserves the death penalty because they are criminals and "trash." What if a man was in such a condition that he had no choice but to steal a loaf of bread to feed his starving family (see Hugo's Les Miserables) - he may have broken the law and may be tried as a criminal, but is he somehow "trash" that deserves to die? I highly doubt that. Your viewpoint takes on a very slippery slope that will not end well morally or ethically.
Again, like the LOTR quote Cesare posted - there are many who deserve to die, and many who deserve to live. But can another human being truly deal out life and death to another, even in the supposed name of justice? I sincerely hope not.