Why do x amp rated consumer electronics often come with >> x A rated BS1363 fused plugs?
The purpose of the fuse is not to protect the product, it's to protect the wiring &mdash; to keep it from getting hot enough to start a fire. The fuse is rated according to the gauge of the wire. The only connection with the actual power consumption of the product is that the wire gauge must be selected to support the expected power draw.

The same thing is true for the circuit breakers in your house. They exist in order to keep the branch circuit wires from overheating in the walls.

In most jurisdictions, the minimum permitted wire size is established by regulations. For example, in the USA, the minimum gauge for house wiring is AWG14, and the minimum gauge for product line cords is AWG18.