Due to extreme amount of heat, the rain water that falls on the dessert will quickly be evaporated. To collect more of it, usually the roots of the dessert plants are really close to the surface
If the plants are close to each other, they simply won't be able to collect any water, so they spread evenly throughout the dessert
Desert plants are widely spaced because of the lack of water in the deserts. They are highly adapted to manage to get every drop of water, be it through their roots or through their leafs or thorns. They have very big root systems, that are both very deep and very big in diameter, so it is practically impossible for them to be next to each other because their root systems are so big and also the lack of water and nutrients, if they are next to each other they will not be able to survive because while competing with each other none of the plants will be able to satisfy its needs.
