If the cable overheated, there could be a fire. The fuse prevents that happening, because its thin wire will melt and break the circuit long before the cable itself can heat up and burn. Some cars have only two fuses. One rated at about 30-50 amps protects components wired through the ignition switch — flashers, wipers, heater-motor and instruments.
Most are wired through the ignition switch, so that they work only when the ignition is switched on. This prevents you accidentally leaving something switched on which might cause the battery to go flat.