To address the argument, it's not fair to assume that recipients of such threats would be either willing or physically able to respond. People with kids will not go around dueling people in the modern era. In my opinion, it's nothing more than a fantasy world. We have a justice system and law enforcement officers. Maybe they don't do a great job, but it should in no way fall to the individual, no matter how zealous they may be.
The point again is not so much that 'this will solve the problem' as 'threatening people should have a significant cost' and this is one way of significantly increasing that cost without needing to appeal to state actors whose alacrity and integrity may be open to question.
This approach maximizes free speech while providing the targets of objectionable or harassing speech more options for responding to it.
Currently you shouldn't use deadly force absent a reasonable fear that it is about to be inflicted on you. But since it is entirely possible to send a threat like I know you live at [address] and I'm coming to [do crimes] and place the recipient in a state of continuous uncertainty, the very open-endedness of the threat manifests the fear of imminence in the target. Rather than making the victim devote resources to continually monitoring and assessing the behavior of the threatening party, we can simply expand the target's right of self-defense in proportion to the scope of the issued threat.