For many users, Youtube is the only video publishing site, and many people get their news through YT. Very few people are aware of the existence of LiveLeak; it is an ineffective platform for spreading awareness.
Would you prefer to stumble across those on Youtube?
It seems better that material which needs to be kept for history and remained uncensored due to advertising is on a site dedicated to that instead of a site which most people use for videos of recipes, memes, and great football headers.
Yeah, there does need to be some sort of inhibition against highly traumatizing content, it should certainly not be promoted to people who do not seek it out. But purging news videos of statues being destroyed and ancient buildings being demolished, is going too far.