The fuse in both cases is only required because the equipment being used is too small for the ring circuit protective device. Plus it limits the total load to 13A - likely sufficient from what you state but not always the case.
Use adequate cable and accessories and the fuse would not be required.
The fuse is not there to protect the equipment
or the cables connected to power it. We are getting into fine definition here, but the fuse is there to protect anything downstream of the fuse from receiving power under fault conditions which will provide energy to enable or support combustion and as such endangering life from the spread of that combustion. It is also there to protect personal from electrocution under fault conditions in the case of an Earth fault.
Some equipment powered by electric power does not have any form of separate isolating protection under fault conditions, such as Luminaries and the sole means of protection is the Fuse.
Even other equipment has badly designed protection under fault condition, as an example the Clothes Drier fiasco which resulted in house fires a few years ago. The fuse is there for the protection of life which is endangered by the spread of combustion initiated by faulty equipment down stream of the fuse.
Clearly by removing the power to to the fault, a secondary effect is the protection of the Equipment and the cables but the primary requirement is the protection of Human Life by either electrocution or Fire.