Plug getting really hot? Is it normal?

[EFLImpudence]

So now you are self defeating your own statements, Initially you say a 3A cable is safe to use in a Shuko fused at 16A but then you say it's not safe on a 32A fuse.

I didn't say that. They wouldn't use a 3A cable.

You asked when a 3A fuse is necessary.
One would be necessary for a 3A cable plugged into a 32A circuit - IF the appliance could cause an overload and/or the fault current would be enough to damage the cable - but in practice when would one use a 3A cable?

You have a 1.4kW Henry - 5.83A @ 240V - on cable rated at 6A by BS7671 but not by the manufacturer. Therefore strictly speaking for BS7671 this would need a 6A fuse unless you can use omission of overload regulations. I am not sure if start-up would cause a problem but it was probably fitted with a 13A fuse anyway so if fault current is satisfactory on a 32A circuit then the 13A fuse is not needed - even more so for a kettle.

So how have you defined the cut-off limit for potentially overloading a cable.

Which appliances can do that? Not the usual fans or boilers or lights where a 3A fuse is said to be required.

I'll come back on your question and ask why we need any fuse, or why 13A is not suitable for all applications.

Perhaps we don't and perhaps it is.

At the moment I really don't know what your comments and questions mean. But I don't think our ideas/ideals are far adrift from each other.

My only question was why do they bother making 7A BS1362 fuses?