I understand that a zoo is an obvious hotspot for photographers because you can get close to wild animals and get some good pictures of them. Or maybe it is just because I dont like seeing the animals stuck in their cages.
Zoo photography is one of my projects, but I don't do it to take pictures of the "wild animals".
First and foremost, zoo animals are NOT wild animals, it is important to understand that. Virtually none of the animals in American zoos have ever lived in the wild, and with obvious exceptions many could not live in the wild because they have been domesticated.
Zoos are great places, but I think a lot of people miss WHY they are great places. Zoos are today's Noah's Ark. They are the only chance that many of the species that are held in captivity will have of surviving long enough until mankind develops enough brains to figure out we don't really need to be wiping out most of the species on the earth.
Zoos maintain genetic diversity that can be back-bred into the wild population. Zoos are an opportunity to showcase the vast and amazing diversity of life on our planet to a bunch of people who otherwise would never be exposed to it. As the legendary Senegalese Conservationist Baba Dioum famously said, In the end we will conserve only what we love. We will love only what we understand. We will understand only what we are taught." Zoos are a way we teach.
That is why I do my zoopictures project... not as a way to take "cool picutres of wild animals", because they simply are not wild. I don't just take pictures of the animals either, I also take pictures of the displays that they are in, both good and bad... I don't try to hide the caging, because that is a part of the whole story.
If I were in your shoes, and I felt the way you feel... with the press against your heart about the caging and captivity of the animals, the bewilderment about the big lenses and all the other visitors... I would take that emotion and take a camera out and try to capture what I was feeling through my lens. If that means going counter culture to do it, then perhaps I would grab a $4 35mm point and shoot and then have the negatives digitized (including a self portrait of yourself at the zoo with the camera via reflection or whatever). If you have feelings about something involving your camera, isn't that the time you WANT to be shooting pictures... that way you can have not only something to show, but something to say.