Having fuses close to the power source helps to ensure that a short anywhere along the power lines will blow the fuse instead of shorting the battery.
If the fuses are near the radio, for example, and you short the wires near the battery, there will be no protection to stop the short circuit from damaging the battery.
On the other hand, if you fuse near the battery then the short could only really occur between the fuse and the radio which would cause the fuse to blow. The blown fuse protects the radio from any damage and the battery from exploding.
In car installations, you'll often see three fuses for a mobile radio. One fuse on each power line near the battery, and a third located on the positive tail coming out of the radio, before the OEM connector that mates with the longer wiring harness. This is the safest solution.
-Adam, KG6JLG