Like a decent plot, for instance.
City of the Living Dead would only be diminished by a plot. It needs to function as a kind of delirium of the senses. That is its biggest selling point. That it drifts away from any standard story telling practise. It can't be restrained by our futile logic.
For me, film is inherently an imagistic form. And the medium it plays with is the manipulation of time (through editing, either elongating or abbreviating these moments caught on film). That is the core essence of film. Then there is, of course, all of the accoutrements that come with this--sound design, acting, special effects, costumes,score, cinematography. And while it is also obviously an extremely effective tool to tell stories, narrative comes dead last in my books. It should only be dusted off when you can't make the rest of these elements work on their own. Essentially, story is a binding agent. It orders things logically, gives us goals to root for and offers us dramatic beats to feel specific feelings. And, as a basic film romantic, I like to believe film works just fine without any of this.
Many of the greatest filmmakers in my book can either push narrative into the background, or forgo it entirely. In really good hands, story telling can be an artform in itself. And that is really really great when it happens. But, sadly, narrative has become such a redundant and lazy thing over the years, I've never found many directors incorporate this element with any particular grace. It's mostly used as crutch. And when used this way, it also becomes an anchor that pulls down and drowns the work of what is pure filmmaking.
Not only do I not think Fulci would benefit from any of this kind of structure, I think he would only suffer from it. You start using narrative in hopes of putting something like City of the Living Dead in proper sequential order, with very clear goals that the characters need to achieve, with things we are supposed to root for, and it turns all of its madness and violence into outgrowths of a (most likely) standard story about the end of the world. Fulci instead allows the movie to be
about the madness and the violence. And to sell such a thing, it needs to be impenetrable and confusing. It needs to feel like a merciless onslaught. It needs to be something you can't really talk about in concrete details, only in abstracts. It needs to dissipate like a nightmare when it's over.
tldr: Fulci must run wild. Stories shant tame him.