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.
There are many fuses, each protecting a small group of components, so that one blown fuse does not shut down the whole system. Many of the fuses are grouped together in a fuse box, but there may also be line fuses in the wiring.