Why? Because its there! (Paraphrasing whoever said that about climbing Mt. Everest).

I think I could still keep it narratively realistic (there would still be chances to roleplay (some elements would be changed, but many could remain surprisingly similar), as well as good old fashioned killing bad guys and taking their stuff). It would be different. It doesn't have to be a utopia (far from it -- I want demons, undead, evil cults, barbarian raiders, assassins, etc.), I mean, there would still be conflicts between cultures (similar to the English vs. the French in historical Europe, or the Chinese, Japanese and Koreans in historical Asia, before they all became enlightened and saw each other as equals in every way)

, and even forms of racism (of the elf vs. orc variety, rather than within a fantasy race). I think that accents and styles of dress might become markers of an "outsider", rather than appearance (within a race).
Diseases (much hand-waving ensues) uh....magical side-effects of gods interfering in the creation of sentient beings by the other gods. There we go.
Hmmm...I think that if 80% of the population is bisexual, and if genetics do not determine child characteristics, then the "gendered" reasons for a man to "spread one's seed" would be nullified somewhat, as well as the need in a woman to find the "perfect parent", since in a group setting, different people could take up different roles, and thus between them do whatever a single "perfect parent" could have done. The connection would be to the children raised, regardless of who biologically fathered (or, after the first two years, mothered) them. Thus I am not sure that such societies in the campaign world would have to go the "one alpha male" route. The CE wolf-pack stuff of Takyris might be on who gets to have sex, and other priviledges.
As for population control...hmmm...some societies would voluntarily reduce pop, while others would try to grab more resources and thus be more warlike. Well, that gives lots of room for military campaign style games, I suppose. As for the "child to adult" ratio, as well as the "child who lives long enough to have kids to adult" ratio, I haven't worked that out. I would probably set the latter at a close to even rate, but slightly positive, to add to the conflict a bit (the usual "humans want to build cities/farms, elves want to preserve their sacred woods, orcs want EVERYTHING", kind of stuff, no real surprises there).
Interesting thoughts. Keep em coming. I am an equal opportunity yoinker and will steal some ideas, and get ideas of my own from responding to other ideas.
I was thinking of children coming from a different source, but am not sure about that. I think I will stick with the pregnancy route for now. On the other hand, I guess there could be an adventure involving catching the bandits who are over-hunting the storks that leave babies on people's doorsteps.
Oh, as a side-note. This would be part of the campaign world-description, but the adventuring party would be more concerned with adventure stuff than with the sex stuff. I mean, while it may establish itself as a topic if a player pursues some roleplaying angle, it wouldn't be a major focus of my campaign. Didn't want to give the impression that I am trying to run a hedonistic-styled campaign. Nothing wrong with that, but not the style I am going for. (Mine is a bit more focused on good guys vs. bad guys -- quite traditional, really).