Personally I never really understood why Light just killed every criminal. I believe that capital punishment is only applicable in certain cases, for instance intentional murder, it should'nt be used to kill criminals like thieves. To me it would make more sense if Light killed criminals that are repeated offenders of assault, human trafficking or rapists.
For some reason criminals like rapists, are allowed to go back to society after spending time in jail. To me this is pretty messed up because the rapist have runined the victims lives, and in some cases lead to them commiting suicide. All the punishment the rapist gets is to be thrown in jail, where they will have a roof above their head, and get fed. This a luxury in numerous poor countries. After all that, they still might be allowed back into society, so Light using his death note to kill off these types of criminals is justifiable.