When I visited the White Oak Conservation Center in Yulee, I was one of the only humans, apart from the members of the staff, that the animals would have seen that month. Visitors to the center are allowed only by appointment at select times. The Smithsonian Conservation Biology Institute is closed to the public on a even stricter basis. Other members of the Conservation Centers for Species Survival coalition, such as the San Diego Zoo Safari Park, are fully open to the public.
There are tremendous advantages to a C2S2 center being closed to the public. For one thing, the facility can devote its resources solely to the animals, without having to think about visitors. Animals can be left in relative peace and quiet to reproduce and raise their young without the disturbance of the public. This is of obvious benefit to shier species.
By not having the public interests to satisfy, the facility can focus on conservation priorities. Zoo visitors enjoy seeing some species of ungulates, such as camels and American bison, and many zoos comply by exhibiting those species. In contrast, many species of high conservation value are less impressive exhibit animals. They may be smaller, or less attractive, or more cryptic. Reptile houses in conventional zoos place emphasis on alligators, giant tortoises, large snakes, and other impressive "show" species. If zoos were to devote themselves solely to conservation breeding, most zoos would feature an entire house devoted to freshwater turtles. Similarly, the value of the C2S2 centers is in having large numbers of individuals of a species to facilitate breeding efforts. In a zoo, however, the attraction of the facility is in having a wide variety of species on display. In that case, a large tract of land which might be used for a single herd at a C2S2 center might be split up among several exhibits at a zoo.
Lastly, critics of zoos often disapprove of zoos displaying animals to the public, thinking that it turns the animals into props used for entertainment. Additionally, charging admission leads to accusations that zoos profit off of their animals, even though most AZA-accredited facilities are non-profits. Being closed to the public reduces the impact of those charges.
Despite these many benefits, I wouldn't rush to recommend that every zoo and aquarium close its doors except by appointment. One of the major benefits of zoos and aquariums is their ability to reach a larger audience to teach about conservation issues and raise support for saving species in the wild. As wonderful as White Oak and Front Royal are for a conservation breeding perspective, they can't do that alone. Nor can they do it without one of the most important parts of the zoo - the visitors.