While the analogy between reproduction and eating seems like a valid one on the surface, especially since some of the openings you describe are shared between these functions, there are some good reasons for leaving reproduction just the way it is. While there are some potential benefits, the cost would be significantly higher in terms of health of the organism which is probably why it has never occurred in nature (at least within the sphere of research I've read).
The potential benefits seem obvious; for one thing, you can birth an egg or child from a much larger opening than the one in which the gametes or sperm enter, meaning that you lose a lot of the complications in modern mammalian birthing, particularly in humans where increased brain size is causing complications that evolution is trying to solve through bringing babies to term at a much lower level of development compared to other species, and neural 'specialisations' in the form of Neurodiversity, or the Autism Spectrum. Certainly birthing would be much less painful for most species designed this way, and you could keep babies in utero for longer, right?
The trouble is, for all but a very specific set of organisms, the problem that you have with this is frequency of use. You've just added significant complication to the design of your organism for something that doesn't get used all the time. Having a mouth and an anus makes sense because food is common requirement for us. Most organisms, especially the complex ones, feel most comfortable if they eat daily or more often. So, both openings are going to be under constant use. The hygiene factor alone makes two openings and a through system sensible under that kind of workload. Reproduction on the other hand doesn't happen nearly so often and as such can cope with the simpler system as the single opening is used so much more rarely. The IO (if you will) just doesn't justify the increase in complexity.
It's been my experience that evolution favours simplicity wherever possible; specialisations do occur but they also die out quickly when the conditions change that led to them in the first place. In this instance, there would be some benefits to this change to be sure, but the existing system works well enough that it is less of a concern than the eating example you gave in the OP.
Humans are the embodiment of that principle. We are generalists in almost every sense of the term. We are not the fastest animal but we can run. We're not the best climbers or swimmers or trekkers, but we can do all those things. We can eat nearly anything compared to most other mammals, and the few specialisations we seem to have are being able to throw things and work tools, which when combined with minds capable of rapidly adapting our behaviour through better knowledge of our environment, has seen spectacular results. And we've done it with the simpler reproductive plumbing you describe.
In short, the added cost in maintenance and hygiene isn't worth it for a system that works well enough as it is. While it is possible that we would get reproductive benefits, the added maintenance would more than offset the those benefits which is why (I suspect) it will never happen.