Killing another human being isn’t a pleasant thing to do even if it justified. I don’t believe this serious business should be reduced to the level of entertainment that appeals to the basest human instincts, nor is it a suitable sight for children.
People don’t need to see it to be aware of the fact that it happens and that it would happen to them if they were convicted of murder. Public executions would have a brutalising effect on the spectators which would lower respect for human life, which would not have a positive effect on reducing the murder rate, but quite the contrary. It isn’t simply fear which reduces the murder rate. People have to think decently in the first place....
I would point out that the Roman Empire had very public executions and you didn’t really have much higher violent crime rates then in modern American cities, at least not before the Crisis.
Most of the murder in the Roman Empire was political murder and restricted to the political classes.