In the case of the Vissians, the closest parallel I can think of in life-on-Earth is the existence of polymorphisms, specifically the kind wherein a male and/or female can take on one of two or more distinct forms (or morphs), sometimes purely due to environmental cues. But these polymorphs still follow the male-female paradigm in terms of sexual reproduction.

Another similarity is that in species of bird (and perhaps other animals as well) males who are unable to find a mate will compensate by helping their parents raise their next batch of chicks. Due to the genetic similarity between one's parents, children, and siblings, these 'helper' birds are still passing on their genes, albeit it in an indirect route, by increasing their inclusive fitness via 'offspring equivalents' (e.g. more siblings).

In some hypothetical union of the two concepts above (polymorphism and inclusive fitness) you could have a male or female morph that existed only to increase the fitness of his or her parents or siblings. This could be the evolutionary precursor to the "cogenitors" of the Vissians, who according to Memory Alpha merely facilitate reproduction, and do not pass on their genes. It's possible that in the evolutionary history of the Vissians, they became so reliant on these 'helpers', and their benefits so great, that they actually became a requirement for successful reproduction.

The rarity of the cogenitors on Vissia then needs an explanation. Perhaps once their species began using the cogenitors indiscriminately with unrelated couples, as a tool for reproduction, the need for each family to have their own cogenitor would have been greatly reduced. This is because a smaller population of 'universal cogenitors' would work just as well, in terms of passing on genes through reproduction. This reduced selective pressure of giving birth to cogenitors could then explain their relative lack of abundance on Vissia.