A house takes up a lot of land that would have been space for a wild garden to grow. However, the plants of the desert are limited by water availability, so if you effectively make use of the rainwater that falls on the roof of your house, you can mitigate the loss of space. The additional water allows more plants to grow in the remaining space.
A house produces other sources of water that can also be used to supplement a garden. These sources in include greywater, AC condensation, and runoff from driveways and hardscape. You may find that there are abundant sources of additional water that you can harvest for growing a wild desert garden! In the pages linked above I describe the techniques I have used to harvest water for my garden. I also discuss drip irrigation, which is the most efficient and effective method for watering plants in the desert. Below I included the water use at my residence in Tempe. I typically use 15-19 hundred gallons per month. That can be compared to the average Arizona residence which uses 75 hundred gallons per month. So there is a lot of opportunity to save water!