Well, we have
some knowledge; we know for a fact NZ has censored the manifesto and recorded video stream of Brenton Tarrant, the guy who elaborately planned and carried out a massacre of 51 people at a mosque in Christchurch. I believe they've done the same for stuff like ISIS and other terrorist materials, but I don't know the specific details of that.
In the Tarrant case we do know: the manifesto (not too hard to find) is about equal parts polemic and roadmap/planning document. The video recording is from a helmet-mounter camera and basically looks like a first person shooter video, except that all the targets are fleeing civilians. It's not impossible for people in NZ to see these materials; academics, journalists and so on can apply for permits to obtain and possess the material. Absent that, possession is, as I understand it, a crime, but one with a very low chance of being caught. The primary intent of the law is to have a strong sanction to prevent people distributing it and inciting similar incidents in the future.
I'm not convinced that forcing the materials fully out of circulation is a foolproof preventive strategy, but it certainly creates barriers to the acquisition/ collection of such material by wannabes, and collecting this sort of material is definitely A Thing among other mass shooters, who are quite a bit more social than most people imagine and have an online community of sorts.
So the free speech argument generally goes along the lines of 'we don't know what we don't know, allowing the free flow of ideas is the only rational way to ensure freedom of life and the discovery of new ideas without inhibition.' But from NZ's point of view, they definitely don't care for a repeat or innovation in the practice of massacres, and the surviving relatives and neighbors of the dead presumably don't care to see the murder of family and friends become a an entertainment commodity or be weaponized by trolls who use the material to traumatize them further (please, let's not pretend that this doesn't happen). And they've balanced their prohibition with exceptions for serious analysis and study with a straightforward application process, albeit a subjective one that is administered by bureaucrats rather than a mechanical system.
So there's a concrete example, with come added context (sorry, it's late and I'm not at my main machine so I'm not going to dig up a pile of links/documents to flesh it out to article quality). So, should we accord any weight to those considerations, including the exceptions, and if not why not?