But, to just quickly make the argument the author would have thought to mention if they had spend five minutes on Google and were intellectually honest: CNs aren't intended to allow you stop reading, although that may be an option for people that really want to.
Their primary mechanism is different: it's a quick, easy, and, for those who don't care, totally trivial signal to the readers that the writer or speaker is aware that the content may trigger strong emotions, but that it isn't their intention to inflict any harm.
It's a tiny gesture that, for those where it matters, makes a whole lot difference. If you can't quite follow along, just imagine how different it feels if someone intentionally punches you compared to inflicting the same amount of physical harm inadvertently.
If anyone is being overly emotional, it's those who are somehow incensed by others' attempts to avoid harming people. I'm not especially harmed by reading about violent rape, but I can easily understand how someone might be. How its possible to deny that, but get all enraged about a single line of italics at the top of a five-page story is, unfortunately, beyond my abilities.
Neither, by the way, is it censorship. It's the opposite, a mechanism allowing people to make informed choices, thereby expanding the universe of possible content that can be used for any given purpose without fear of offending or harming anyone. If you somehow managed to abolish the MPAA rating system, you wouldn't get more of the movies that were previously rated R. You'd get none.