While I do agree with your statement, I don't think it would be feasible to do that. Most visitors go to zoo to see well-known animals, or animals that are active and charismatic. Also, most visitors aren't going to go to a lot of zoos in their life so the rarity is not an important factor for them.
Maybe for some animals it may work, with a bit more advertising and public image. Take the example of fennec fox or meerkat, whose interest increase dramatically. But both of them are playful and unique animal, which make them good animals. In contrast, while seeing e.g. marbled cat in captivity is incredibly rare for us, most of the visitors will still think it is a normal cat, with not much difference as the domestic feline. These happen way too often.
Remember that "normal" zoo guest aren't us. They wouldn't care about rarity or such. "SDZ is the only place in the US with Tongan megapode." So what? It's just a normal pheasant by normal zoo guest. Even if visitors know they're rare, they still probably don't bother seeing them. They want to see animal they can see on TV, they want to entertain themselves with what they know.
Even inside us zoochatters, there are still a lot of us who are missing out on rare species. While I fully admire those who seek for every rare species out there, I can't see most of even us looking for e,g a rare species of stick insect or a rare variety of coral. To let normal visitors enjoying rare species is possible, but it will need a lot of work.