Texas

Correct, not even for serial killers. Police are not judge, jury, and executioner. They apprehend suspects, and the courts first prove that the suspect did the crime beyond a shadow of a doubt, and then if found guilty the courts decide the punishment which cannot be cruel and unusual and the punishment must fit the crime. For murdering 1k families it would be life in prison or the death sentence.

When the justice system was founded it was established with a number one priority of protecting the innocent, with a priority of avoiding false convictions. Otherwise, a king with absolute authority could order you to be executed by pouring molten metal down your mouth and on your face for the crime of ~~flipping him the bird.~~ your neighbor accusing you of talking ill of the king even though you never said anything of the sort.