Livestreamed or not, this is immoral and Australia are quite right to try to block it. All countries should be seeking to do the same.
It prevents at least one person from ever doing crime again
I see the same arguments made about long prison sentences. It doesn't do anything as a deterrent to others so it's useless!
That's only true if the goal is deterrence. Not if the goal is simply to lock a criminal away from the rest of society so they can't do more crime
That all said, I'm not in favor of public executions making a comeback.
2. People who believe in martyrdom will never be deterred by this. Many grow through adversary, look at the Houthis.
3. There is no proof that it even works on ordinary people with the opposite effect sometimes taking place (brutalisation), it is a terrorist strategy. If it worked, you would see more countries doing it.
That can be changed if you live stream it and then it becomes deterrence