Most of the objection to television executions seems to be that it's... distasteful. Gauche.
Many agree that execution is fine, so long as it's done behind the scenes.
But our culture has a tendency to sweep aside anything that makes us uncomfortable, as if hiding something erases its moral impact.
However, insofar as executions deter other potential attackers - they should be televised.
And yes, insofar as executions represent our society taking the life of another human - they should definitely be televised.
We don't like to see the sausage being made. But that doesn't change the fact that a pig is slaughtered.
We don't like to talk about casualties of war. But that doesn't change the fact that almost any choice made by our political leadership will result in the deaths of innocent men, women, and children, somewhere or somehow.
We sanitize language surrounding abortion. As if referring to something as "healthcare" changes the reality of killing and dismembering a human fetus.
Televising executions isn't about entertainment, and it's certainly not about bloodlust.
Instead, it serves two purposes.
1) Deterrence.
Just as seeing images of rotting lungs on cigarette cartons is a greater deterrent against smoking than simply knowing about cancer, a public execution is clearly a greater deterrent against crime.
2) Responsibility.
It's no small thing to sentence a man to death. And if we, as a society, are to execute people (which I think in certain cases we should), there should also be absolute clarity over what that means. The death penalty should never be reduced to some bureaucraric process with its human element erased.
Hiding our executions doesn't make us more civilized than ancient civilizations, it just makes us less transparent.