I think you've made some good points.
Generally, I am not for censorship except hate speech, images of people being brutalized or killed, and senseless violence. The latter seems to be a catch-all, but the repetition of violence across all media at all times is, as you note, desensitizing. After a couple of decades of nonstop violent depictions on TV, video games, movies, social media, etc., and look what the result is — a nation full of people who cannot find a way to be civil to one another. Is this the world we want to live in?
People are generally unaware of the damage that hate and violence wreaks on the psyche.