I'm not against governments passing legislation that promotes and furthers animal welfare, but only if that legislation is the result of well-informed advice from respected scientists and animal care professionals... and that is not always the case. A good example can be seen in the Circus Cruelty Protection Act passed in California, explained and referenced in this thread:
California’s Circus Cruelty Protection Act. It would have had quite a negative impact on using animals for educational outreach offsite. Fortunately, after receiving public feedback and meeting with representatives of affected institutions the legislature amended it to only apply to circuses, the initially intended target. Government intervention is sometimes necessary, but needs to stem from cooperation with legislated institutions, not from misinformation campaigns produced by a vocal minority.
To contribute to the more general debate: zoos are not going anywhere anytime soon, although certain species (like cetaceans, and perhaps elephants in the future) might experience a different fate. Zoo support is high; additionally, while I've had several friends and colleagues who are skeptical or disapproving of zoos, they are far from radicals, most have outright said they don't support PETA and consider them sensationalist, most have admitted that zoos serve an important conservation role for some species, and they generally feel much more strongly about factory farming and puppy mills than about zoos. Some of the evidence they offer for their positions is dubious, and they have generally been receptive to my counterarguments. I agree fully with
@Batto that persuading the general public through outreach and education will be far more effective than giving oxygen to radical organizations.