I know they have space for large amounts of species but that isn't stopping institutions in those states with less space from having a few of those species. California and Ohio are two of the best states for zoos so what is the excuse there? And we have no space in the AZA for any exotic deer species?
Also, it isn't impossible to have many small populations instead of a few large ones?
That completely misses the point of having group populations. Most of these species are herd animals, they do better in big groups. Larger herds also facilitates more breeding. Given there's so many laws regulating hoofstock, as Argus mentioned, it's much harder to parse out a few here and there and then bring them back at breeding time, like is done with some carnivore species.