The best desert house would be actually dry shrubland. They are deserts for geographers and locals but not biologists: Sonora desert, Mojave Desert, Kalahari desert, Australian deserts etc. They have very catchy succulent plants: saguaros and other cacti, baobabs, giant euphorbias, ocotillos etc. True desert should be little except sand.
Perhaps their problem is that zoo people automatically think about big ungulates, and overlook that smaller animals and succulents could make a very good exhibit of its own.
I once imagined an exhibit based on Madagascar spiny forests:
If I Had My Own Zoo
PS. About Desert Dome in Omaha - this one has much too small exhibits and little natural substrate for digging animals like meerkats. Although it could be wonderful if remodelled as a pure reptile house with large monitor lizards, large teids and agamids, large tortoises, further venomous snakes, maybe desert / sacred crocodiles etc.