That seems like a good idea. If they really want to execute someone, make the official of the state shoot them on video. I'm guessing capital punishment would be almost zero within 10 years, because nobody wants to be seen as a cold-blooded killer, especially when they know that people could review the video.
Nah instead two elections cycles later a candidate will be elected, who will be running ad breaks and monetizing execution videos, all while parading patriotic bullshit.
This would backfire as you'd see people voting for right wingers more because it's "Cool and manly to kill people", you'd also get the foot in the door for legalized bloodsports.
Yes, there was a moment in very beginning about the duke carrying out executions personally and making his sons watch, because that's his responsibility.
Guilt for administering a death has been thought of before; that's part of the reason why there's a firing 'squad'. You have however many people with lethal rounds, and however many people with dummy/blank rounds, so nobody knows for sure whose bullets were live & killed him.