You got 2 & 3 wrong: Bullies will see that authority punishes victim, learn that their behaviour must be right and the victim is actually the guilty party, whatever they do. Bullying will actually spread as other people join in on this clearly positive activity.
And yes - even if the victim is physically injured in fron of authority with the injuring party loudly declaring they did it on purpose - the victim will be laughed at and then punished by authority for being injured.
Humans are social pack animals and creating a pariah and treating him/her properly is part of pack behaviour. Suck it up.
What I have always found odd is that while it is perfectly acceptable and even praiseworthy to make someone wish they were not existent, it is very reprehensible and egoistic for that person to actually terminate their existence. I've asked for explanation but the only one I got is that it makes the bullies feel bad.