First of all there's no justice here because justice would be him being killed 13 times, and then also injured 30 times commensurate with his actions. Second, there are very good reasons to make it public and livestream, transparency, finality, showing the death penalty actually does occur without 30+ years of appeals and delay (see botched execution lady), showing the public that this is society's choice, depussification of America, depussification of the military, restoration of some modicum of trust to government to actually do what it said. You may not agree with them, but just ignoring them isn't honest.