But if any of the abuser's allies did anything to the abused, they could be easily identified and tracked down; this could act as a deterrent.

If we're not capping the level of abuse it could easily be too late though. Let's take it to the extreme, somebody wants to kill you and you have no choice but to broadcast your location to everybody. Some people receiving that data, you don't know who, are happy to do the killing for the person who wants to kill you. Afterward they can be identified and tracked down, but at this extremity it's too late.

The punishment for killing is the deterrent.

For people that have rational minds. What about people who are irrational or have some sort of mental illness? I guess that's just a "too bad" for the person who is now dead?

Yes its too bad when I'm dead. I could done anything I could have done to prevent that but there will always be somebody who are irrational or have some sort mental illness or anybody who could eventually find a way to kill me if they really want to. This is happen in open or private society.