Extremely few humans are killed by captive-bred exotics. It's reasonable to take some risks for a measurable gain. In some way or another these animals are worth a lot of risk to some humans. Environmentalists insist that tigers, lions, chimpanzees, and other animals that can kill humans be allowed to run free in their native habitat which also happens to be the native habitat of humans. That's a lot easier to sell to people who are willing to let Africans deal with lions and chimpanzees in their backyards, and East Indians and Chinese deal with tigers in their backyards. Any English-speaking culture tightly controls its predators, using lethal means, and calls that "conservation."
Myself, just in the interest of fairness, I believe that the risks that a person or group takes should be similar to those that we ask of others. The question of whether this kind of risk should be taken has already been settled in the minds of animal rights activists and environmentalists who advocate the sharp culling of the human race or its total extinction. That bit of information doesn't really process. It's hard to take in. Add in the contradiction when they scream at us that we just can't keep exotic animals as pets because it's "too dangerous." Sort of causes a brain seizure, doesn't it? That's why adults make their own decisions.
Everyone wants the animals to be saved and everyone wants someone to take some risks and spend some money to do it. Most people don't want it in their backyard and some of us find out the hard way that they think that my backyard is their backyard. Once the fear button is pushed they don't want it near them, they don't want to process it in their minds, but they still want someone else to do it and will pay them to do it. That's how we get "sanctuaries" that promise to keep the allegedly dangerous animals on small reservations. Just send them the money and they will put them on display and only breed what the government says that they can breed, and they can explain why it's best for the animals too, even if it contradicts established science and experience.
Why take the risks at all? It is because there is an ethical sense that most people have that says that we don't have to make extinct the creatures that sometimes inconvenience us and even kill us. We think that fair is fair. We also like the creatures and benefit from their company even when we don't use their physical carcasses for food and useful materials. For their benefit, humans can farm tigers and just about anything else so that their numbers remain stable or even grow. On at least some of China's farms the tigers die of old age before they are used for materials. The market for tiger parts is just going to have to do without wild-caught tigers. Not that the wild is going to exist much further. Americans seem to demand a buffer zone between us and the wild animals that's larger than some countries, so you can't even count most of what's outside of city limits. Other countries are growing even faster. We either find a way to breed in captivity or we lose them as resources and we lose their ability to live for their own sakes.
One side of this controversy produces large numbers of new animals who are quite fit to carry on the species. The other side, the animal rights/conservation side, does what it can to gather up those captive-breds and eliminate them. Which side do you think has the greater ability to preserve non-human life?