I would still use fuse protection when using semiconductors to control as the semiconductor fuse will protect the device, where using a overload or MCB they are not fast enough acting to save the semiconductor. However that is a special case. With a 16A supply to 13A sockets I have not seen a fuse rupture due to a cable fault. Only with a 32A supply to 13A sockets has the fuse ruptured with a cable fault, and often then often the MCB has tripped as well.
I have had fuses rupture due to equipment faults, vacuum cleaner motor burning out for example, however it has not saved the motor is still needed to be renewed, so in real terms the fuse in the plug is to reduce the fire risk.
So if we consider domestic equipment and fire risk, then for a vacuum cleaner limited to 1.6kW or 7 amp clearly using a 7 amp fuse is too small, but using a 10 amp fuse it will possibly rupture that little bit quicker than a 13 amp fuse which could mean it ruptures before it goes on fire. However my vacuum cleaner is very much smaller in size, and when the motor is running then there is no connection to any low voltage supply. One would hope if it eats it's own lead then the switch mode power supply would auto shut down. But it also has a habit of eating any other lead left lying around. It has really tidied up the house. No longer are there phone charging leads left every where, if they are it eats them.
However robotic cleaners can damage leads although in the main it simple stalls and switches off and waits for human intervention to remove the lead. So specially with thin lead sets there is a need for correct fusing. So in respect to lead sets the IEC 60320 stipulates the maximum current permitted. So electric shavers have C1/C2 connector so shaver adaptors should have a 0.2A fuse or other over current limiter. Next is 2.5A and I have not seen a 2.5A fuse for a plug but I would say 3 amp is close enough for C3 to C8. The C9/10 is rated 6A not seen a 6A fuse so as to if a 5 or 7 amp is used I am unsure. Not a HiFi fan so not used one. The C11 to C18 does however raise a question they are rated at 10A and clearly we do have 10A fuses. However the C15, C15A, C16 and C16A are the typical plugs used for kettles. But the kettles are often rated above 2.3kW limit of the plug. So should one use a 10A or a 13A fuse where the connector is rated at 10A?
The C13/C14 is used a lot on computers and is often supplied with a 3A fuse in the plug. However where the cable is not marked with anything which shows less than 1mm² should it have a 10A fuse. Remember when we do inspection and testing of in service electrical equipment the lead set is a separate item to the computer.