Even if it could (and parallel posters argue it cannot), there is a meta-problem: "Who is allowed to post violent content?". Violence is contextual, and also legality of posting it is contextual. Same goes for other objectionable materials (nudity, extreme ideologies etc.).

Point in case, if all users were subject to the same criteria, the big names in media would quickly get banned. And/or would enter war path with Facebook, accusing it of heavy-handed censorship against the freedom of the press.

Same for reportage of popular events with any degree of nudity. A news piece about a Femen protest, a Pride event, a World Naked Bike Ride, maybe even the No Pants Subway Ride would cause a ban.

Likewise, anybody documenting & discussing historical events, and anybody documenting & discussing present-day uprising, revolutions, civil wars, persecutions, etc., would quickly get banned, essentially sweeping a lot of abuse under the rug. Probably even discussion & documentation of domestic violence would have this problem.

As a lighter aside, cartoonish violence (video games & movies) could also easily fall prey to automated violence take-downs.

All in all, Facebook really really wants to give certain users (mostly press & historians) broad, sweeping exceptions to the general rules.