Similar to sheets, a child's mattress gets child off of hard, dirty ground, and provides protection from jiggers.
Jiggers are parasites that burrow in the skin. It is very painful and the only way to remove the sand flea is by digging it out. This is often done with unsanitary tools, which spreads disease. Sole hope has a lot of great information about this pest. The easiest way to prevent jiggers is by wearing closed toed shoes. Schools often treat their classroom floors by spreading cow manure across the floor. (Another reason desks are needed).