He also says that 'no one around here wastes water in this manner' referring to baths and the like, but why would water be so scarce in this entire region of the Delta Quadrant?
We don't have to think it's the "entire region". This, after all, is what Neelix has to say about the matter later on, in greater specificity:
"Kazon sects control this part of the quadrant. Some have food, some have ore, some have water. They all trade and they all kill each other for it."
So first Neelix establishes who these people in front of the landing party are: the Kazon sects are the only players of note around, thus the ones fighting for the Ocampa riches. Then he further establishes that these local forces of said sects trade and kill in order to be able to stay on the planet and wait for their opening. Which then provides Neelix and the landing party with
their opening.
After all, Neelix is not describing the galactic politics of Delta to Janeway in that scene. He's divulging partial truths about the immediate situation on the surface of the desert planet, in order to mislead Janeway into helping him in his personal quest.
So, no water shortage anywhere outside the Ocampa surface encampments (and not even on all of them). But a serious water shortage on this specific encampment, thus a way to manipulate these particular Kazon and liberate Kes.
On this issue, I'm not even convinced that the writers intended the sillier version where the whole quadrant suffers from thirst - the wording is just ambiguous, but the intent all along may have been to describe the situation suggested above. In contrast, the "Elogium" thing is just plain silly by obvious writer intent... But we could explain that one away, too. We just have to note that nowhere in the episode is it actually said that the Ocampa only give birth once!
What
is said is that if an Ocampa female doesn't give birth when the elogium first hits, she has missed her chance for good. But if the first time goes all right, then a second, a third and for all we know a fiftieth try should be quite possible. All Kes and Neelix worry about is the first time, after all; we hear nothing about what happens beyond that.
Timo Saloniemi