I wouldn't say all cichlid species. With some pairing cichlids-- angelfish, discus, severums, guianacara, some types of geos, even some green terrors I've had, dividers are not needed and would be counter-productive, as good pairs will exhibit compatible, bonded behavior that helps them work as a team. Some species, it may just depend on the pair, but some species need the time together to go through the process of forming a good bond, during which time some engage in mock fighting to test the fitness of the prospective partner or they might also fuss while working out disagreements over nesting sites. Some species or pairs may take several spawns to get the process down, and need time to settle in as a cooperative pair. Dividing some of these types would only short circuit the process. All of this can vary by species or particular pair. With some types, how peaceful or how rough they are depends on the pair, but rarely does one kill the other, except maybe in too small a tank or possibly if a pair is so incompatible and you leave them together so long that one stresses the other to death, etc.
Then there are harem breeders, like Malawi cichlids, frontosa, etc. (all of which I've bred) where some males are mean and others not at all, depending on species or individual. Especially with frontosa, things will simply vary by group, a lot depending on the alpha male breeder, which can be mean or mild. But you'd hardly want to divide these fish, they need the interaction as part of the process.
There are Tanganyikan cichlids, like emperor cichlids, for example, where pairs cooperate very well in defending nests and fry and you'd hardly want to separate pairs with a divider, as it would stress them and disturb their natural behavior. Others, like some Neolamprologus and related fish, form cooperative social groups where some in the group are the primary breeders and others act as 'helpers'.
Bottom line is there's a lot of diversity in cichlid behavior and breeding them depends which species you're talking about. There's no one single model that's typical for all cichlids.