It is a very annoying feature of the game. Some animals I can understand - aardvarks, okapi, pangolins, and other naturally shy animals - but others I feel like should have a much higher threshold - flamingos, antelope, primates, and so on. Or, in a perfect world, it would vary from animal to animal (shy animals get stressed more easily, but bold animals don't, that kind of thing).
The reality of zoos is that there are limits on how naturalised the animals can be while still holding to a high quality of care. If you pulled a bunch of springbok right out of the wild, then absolutely you would expect them to be terrified of a zoo-like situation, but usually zoo animals "get used" to their situation. The springbok at my local zoo have very little fear of people, and only startle at loud noises. One of them is so brave in fact that the zoo had to erect a secondary barrier fence because he was letting people touch him through the wire (and, no doubt, feed him).
I've often thought that in-game there should be circumstances under which stress stops becoming an issue. If the animals are in the zoo for long enough, they don't spook as easily, because they're used to guests. If the animal is in a big enough group, they would feel more secure, and get less stressed. Those sorts of little details would make things a lot easier, and a lot more realistic as well. That said, I'm sure there is a game balancing reason for it all. Maybe we should have a Sandbox option for turning off stress (even with welfare turned off they still get stressed) so those of us who don't play for a challenge can have it the way we want it, while leaving the other modes with the game-balancing features.
