You ask a simple, but essentially unanswerable question about zoos and then bale out from the ensuing discussion..?
You have (I assume) chosen a vegan lifestyle and expect others to align with your views on zoos in general and in addition widen the gamut to include farm animals and pets.
Let's face it the elephant in the room (pun intended) is that there are simply too many humans in the world that as a minimum require food and water every day. Without industrialised agriculture, many more millions of humans would die of starvation than are already doing so each day. Perhaps we need to start neutering humans to prevent them from breeding and so they can then peacefully die out after living out their natural lives? Hmm... perhaps we should put that one aside for the moment.
Domesticated livestock has existed for a few thousand years and even though you don't agree with humans consuming meat or using other animal products as part of our lives, that doesn't alter the the fact that we are omnivores and have been doing just that since (and perhaps before) we came down from the trees. Just take a look at a set of human teeth, that tells a pretty good story of the the things we have evolved to consume as food.
I do fully agree that wherever humans 'harvest' animals as part of our food chain, the treatment of the animals should be carried out in a fit and proper manner. On a personal level, we purchase locally sourced meat for our family. We are quite satisfied that the animals are treated in an appropriate manner when they are alive and do not undergo long uncomfortable journeys on the way to their death. Sadly I know that is not the case everywhere.
Some, perhaps many aspects of human behaviour towards animals are abhorrent. Nevertheless, animal products (flesh for food, skin for leather, etc..) have been a part of mankind's livelihood for millennia. Personally, I don't see that changing anytime soon.
To come back to your question about zoos. Ideally, humans would not have trashed the rainforests and messed up other important habitats. They would not have hunted some species of animals to extinction. We are now living in a more enlightened age, where at least these issues are being discussed. I see the principle role of modern zoos to a "Noah's Ark", where we can perhaps preserve some of the animal diversity while it's still there to preserve; in the hope that one day sufficient and appropriate natural habitat exists where the animals can be reintroduced/released into the wild.
100-years ago, zoos were constructed to house an array of curiosities from the wild, for the public to amuse themselves. By the way according to material in visitor centre, the concentration camp at Bergen-Belsen was seen in the same way by the local populace, who while out for a stroll on a Sunday afternoon would peer through the barbed wire fences at the 'inhuman' inmates. So this seems to be a voyeuristic behaviour that is part of our being. Today, there is no doubt that the public curiosity aspect (footfall and therefore entry money) is an important factor for any zoo, but hopefully the animal husbandry and welfare is of a higher standard, and there is a more concerted effort to hold collections that may one day provide an opportunity to contribute to the natural world. In other words, I believe that at least for some zoos, their principle objectives address a higher calling.
Patently I am not vegan, that's your choice, it's not an easy one and I do respect the commitment that goes with that decision. No leather shoes, woolly jumpers, limited choice of beer (actually the biggest issue
), etc.. However, please don't assume that by choosing to be a vegan, you by default own the moral high ground on these issues.
I'm not taking any of this to heart as I know it's an emotive subject so let's get on with photography! 
