To date there is no federal law barring private citizens from owning exotic animals. It is left to each individual state to decide if it is ok for private citizens to own them, and if so, if they are required to carry an up-to-date permit with regular inspections. Sadly, in many states, a permit is all that is needed and there are no regular inspections. The best way to solve the issue to say "no" all the way across the board. A sanctuary or zoo has the adequate funding, resources, and expertise by vets trained specifically in exotic animals such as Jack Hannah, should be allowed to house these animals with current permits and regular inspections (I suggest an inspection every 6 months with annual renewal of the permit and x-amt of Con-Ed hours for ALL staff members appropriate for their position and level of education with an emphasis on safety of themselves as well as the public). Breeding programs should be few and far between with special endorsements and restrictions on zoos that house and breed exotic animals. From what I understand, many zoo breeding programs are often ran by a public or private university with an extensive veterinary program that offers specialized curriculum in exotic animals. These zoos are often funded by taxpayer dollars, private donations, as well as general admissions/merchandise/concessions paid by zoo patrons. Some zoos are able to receive grants for excellent ratings in their programs which helps with funding. They also have the appropriate enclosures to ensure the likelihood of the animals leaving their enclosures is little to none. Should an animal leave it's enclosure, there are preparedness programs that the zoo has in place to quickly deal with the situation.
If an exotic animal must remain in captivity, then a sanctuary or zoo is the best place for it to be. Not in someone's barn in a cage, not in a roadside attraction or circus.
A sanctuary generally specializes in one type of exotic animal. Their downfall is that they are not funded by taxpayer dollars and they rely mainly on private donations. If a sanctuary is not able to maintain the funds it needs to operate - they first seek to find new homes for the animals they do have. They don't just abandon them or turn them loose to pose a risk to the public. If they are unable to find suitable homes for their animals they humanely euthanize them. The animals are never resold to a private buyer. It is always a zoo or another certified sanctuary in good standing.
I'm not sure who came up with the idea of owning a tiger like it is a Labrador Retriever, but it is a really really bad idea.
I say ban all private ownership of exotic animals.