Why should they censor? We the people need to see these things to understand how horrible they are. If you censor this and things like children getting hit by shelling, war becomes OK. And war is never ok.
1) People have the right not to have their corpses, and their spouses' and children's corpses, rubbernecked by a billion people, a significant minority of which will take the opportunity to make jokes about the video.
2) The videos themselves can be seen as a kind of propaganda, both for the violence a person might be capable of and the attention they might get for it. This I'm less sure of: I'd be curious to see if there's a contagion effect.
Why do people have that right? I don't feel that right on behalf of my corpse, and I'm not aware of any legislation indicating as much. What I DO think people have a right to is to not see that content, if they so choose.
As far as being right wing propaganda, the video could be seen as propaganda for all kinds of agendas, but that doesn't automatically call for censorship. Jussie Smollet case is a good example of how right wing violence is jumped on by left wing activists as a means to demonize their opposition, in much the same way an uninformed "Social Justice Warrior" screaming that "all heterosexual intercourse is rape" is more likely to bolster right wing opposition than encourage other leftists to follow suit.
But corpses of minors is almost certainly against the law to show. I know there are a bunch of American laws regarding privacy protection of minors that don't apply to adults (but IANAL so...). That's something I remember from my journalism class: you can almost do any reporting you like on adults, but if children are involved its way, way more legally difficult to stay in the clear.
For example: if a minor commits a crime and is charged as a child, you are NOT allowed to publish the name of the child. This is to protect their permanent record, so that they have a better chance of reform as they grow up. If they're charged as an adult, I think the rules are different.
This also happened outside of the USA. The US has its own laws, while other countries have their laws. I'm sure details are different.
No. Just no. I'm not even going to try to argue with such ignorance. Responding only to register that there are humans in the world who still have a sense of decency. There are some things where you can't just respond with a knee-jerk "censorship bad because muh libertarianism". Grow up.
Why should they censor? We the people need to see these things to understand how horrible they are. If you censor this and things like children getting hit by shelling, war becomes OK. And war is never ok.