Actually I want to talk about chansey and why you never see any happiny in the safari zone.
Chansey raise their young in an area that's not accessible for safari zone visitors, and we make sure they are the only ones able to get there. While the line is known to be able to resist attacks easily, they're still very fragile during the first months of their lives, so they avoid interacting with any other creature. The chansey, of course, still goes outside of this safe zone, but there's always a group of them taking care of the happiny.
Once they're strong enough, the happiny are taken to another off limits part, this time one filled with oval stones. We did not bring them here, they're part of the composition of the rocks found in the area and the chansey know it. They evolve and are led to places with more sunlight and berries by their parents, which coincidentally is the area where they're available for capture.
Individuals like the one I mentioned in my other post know the eggs are easier to take than it would be to capture chansey and breed them, and that there are some people that would pay them a lot for a baby pokemon (and the stones are a nice bonus, as they also reach high prices), so they follow the chansey, use pokemon with moves that incapacitate the parents in some way (paralysis, sleep, etc.) and take everything they can. We obviously don't allow trainers' pokemon inside the safari zone and so far no thief has successfully escaped with any egg, but we're still working on figuring out how exactly they're still getting so far.
Please, do not try to take any egg you find in the safari zone, we do not allow it and you're hurting the ecosystem we're carefully maintaining.