We have a duck at my zoo that looks a little rough. Well, okay, really rough. When he swims - which he does most of the time - he looks fine. Same when he's flying. It's those awkward moments on land, walking from one pond to the other, that he looks like a mess, with one twisted leg dragging behind him as he shuffles along. It's broken - has been for years - and it's not going to get any better.
On a busy day I might have five or six people tell me about it. Sometimes they are scared, other times angry, mostly they're concerned. I always tell them the same thing. He was found as a wild bird with a horribly mangled leg, and taken to a wildlife rehabilitator. The rehabber was able to save the life, but not the limb - it was unable to heal properly, resulting in a bird that can swim and fly, but not really walk. The bird was deemed non-releasable into the wild, meaning that his options were 1) Euthanasia or 2) the zoo. He wound up at the zoo.
As soon as they hear that story, the upset visitors always brighten up. The duck's story went from being a sad one (especially in the case where they think his injury just happened) to a happier one - he was rescued.
The Omaha elephants notwithstanding, rescue cases are the least controversial animals in the zoo. Even zoo-haters are typically glad to know that a wild animal that is unable to survive in the wild anymore now has a permanent home with food, water, shelter, and medical care for the rest of its days. Sometimes, I'm actually forced to spoil a visitor's experience by explaining that not all the animals in the zoo are rescues... but that does lead to some interesting conversations about SSPs and captive breeding.)
They may make the visitors feel warm and fuzzy that they're visit is supporting these cases, but to me, rescue cases are pains in the butt. Often there are medical issues, as in the case of my limping duck friend. Then there is the psychological angle. Zoo animals - those who are born in the zoo and have spent their whole lives there - tend to be fairly comfortable around people. Some may be inquisitive, others aggressive, others timid, but most have seen enough people to know that we aren't always trying to eat them. Wild born animals, however, have much less exposure to people... prior to suddenly winding up in captivity. Many of them never seem to calm down in the presence of their keepers.
For some species commonly seen in US zoos, rescue is almost exclusively the source of animals. Virtually all bald eagles are in zoos because they suffered some debilitating injury in the wild. Most black and brown bears are in zoos because they were found as orphans, or their mothers were shot as "problem" animals.
Modern zoos pride themselves on how the animals they care for are mostly born in their own institutions, instead of taken from the wild. A cynic could ask how much a mission of mercy it really is for a zoo to help itself to a wild animal under the banner of "rescue" (especially in cases of high profile animals, like the elephants). PETA has gone so far as to accuse zoos of using the concept of the rescue to cover up the capture and sale of wild animals (though consider the source).
The fact remains, however, that the wild is a brutal enough place, even without factoring the role that humans play. Animals get orphaned and animals get injured, and, left to their own devices, those animals often die. Sometimes, zoos can provide a second lease on life.