The funny thing is that the murder rate dips whenever violent movies are in the cinema (some researchers checked decades-worth of ticket sales vs the amount of violence in the movies each weekend), probably because when people are at the movies on a weekend that cuts into drinking time. The dip lasts overnight until the next morning. Similar to effects with porn availability (negatively correlated with sexual assaults). Same thing again with releases of violent games (youth violence is depressed for weeks after the release of a big game, because kids are indoors playing the games and not bored, going out causing trouble).
e.g. there's a push-back to eliminate media that portrays stuff that many young males find appealing - sex, violence, etc. But stamping out the media has the same effects as prohibition. e.g. if porn was stamped out then the only way young horny men see a naked girl is to go out and actually grab one. Some people say getting rid of porn would be good because it would force people into "real interactions", which are more "real" and "fulfilling". But hey "real interactions" doesn't necessarily mean consensual or informed. While we call porn "poor sex ed" ... since when did sex ed class even teach sex technique? Porn isn't perfect education about how sex is actually happens, but it's actually better than the alternative currently offered by society, which is effectively no advice whatsoever. e.g. sex wasn't magically better or more fulfilling back in the days we didn't have this stuff. Get rid of porn and the most likely result is a return to the "blind fumbling ignorance" approach to sex, along with more young guys just taking what they want.
Similarly, you stamp out violent movies and games then some of the audience for those will shift to non-violent movies and games, but not all. Some of them will also decide that going out drinking is more fun than sitting down and watching the "allowed" re-runs of Bridget Jones Diary, leading to more drunk violence.