Eh? This topic is posted about the anime, when we're only on episode 5? Well, no real issue. So it's just a general morality topic? Not intended to discuss whether the characters are moral or whether their actions are moral, particularly? The latter is certainly discussable at this time, I suppose. I'm amazed that people have (well, a person has) already made statements equivocating a belief related to morality in Death Note to a religious belief, maybe that paranoia isn't unfounded. o.o
Anyway. I've considered this so much that it's all become too complex for me to analyze in a way that satisfies me.
So, I'll just write about the United States criminal justice system, for now.
Evidence-based police analyses show no connection between the death penalty and deterrence of crime. In fact, "brutalization" and "resetting" are terms to describe how the crime rate may rise for a period of time after capital punishment is administered.
Deterrence requires that the criminal weigh the pros and cons of committing the crime with the consequence which is intended to deter the crime in mind and then make a deliberate decision to commit the crime.
What's the reality? A majority of capital crimes are between people who know one another, many of those are spontaneous and hardly premeditated, and therefore with a severe likelihood that a suspect will be immediately indentified. Detectives clear 86% of such cases (immediate suspect identification) but only 12% of those in which one is not (identified). Murderers who premeditate and thus are subject to deterrence will not be as easily identified as those who don't, and if so will have an 88% chance of not getting anywhere near the death penalty. Not only that, criminals wait an average of 8 years on death row, and the appeals process causes only a tiny fraction of those sentenced to actually... die.
Applied to Death Note, all criminals who commit a crime worthy of media sensationalism are subject to the possibility of immediate and uncontested punishment (that is, Kira's divine retribution).
If Kira were to obtain the cooperation of the police, then he would also have access to cases not sensationalized, and would be to then, for instance, kill absolutely anyone who commits or is suspected to commit a certain type of crime. That certainty, when weighed in the criminal mind, would have a much more significant deterring effect than capital punishment as it currently exists.
In particular,
By the way, note that Light is killing criminals also because he believes it's justice to kill the rotten, not just because of the deterring effect.
Light's moral belief it is not that it's enough to protect the innocent. From Light's point of view, the murders are in themselves just. However, he does believe the act of murder is immoral. Therefore, he is sinning in order to exact justice--which he recognizes. (Probably no one understood this distinction, unfortunately.)