There's no inherent conflict between taking things down and preserving evidence - it should not be difficult for Facebook to "cease publishing" a particular piece of content (i.e. stop showing it to the public) while preserving it in their systems as evidence, together with all the metadata of who/when/how posted or reposted it.

In fact, for the main categories that must be taken down quickly (e.g. child abuse material, death threats, etc) it seems obvious that the evidence must be preserved - why not extend it to all the violent stuff that gets banned.