Seems to me we'd do better to shut the Cincinnati Zoo...
The zoo at this point were just recording the last survivors for posterity's sake.
So do penguins, gulls and terns, yet they can be bred in zoos. Also, the big colonies of the passenger pigeon mostly like where a phenomenon of the 19th century (possibly human induced), the effective population size of the species has been shown to have been in the hundreds of thousands range.
Oh, and the Carolina parakeet was bred in zoos, even in Europe. Unfortunately they weren't that consistent back then yet.