Didn't the OP ask about 433.3.1 (A device for protection against overload need not be provided...) rather than 433.1?
(i) is only needed because 433.2.1 is so badly worded.
(iii) is only for the origin,
so I'm guessing you're thinking about (ii) - characteristics of the load or supply mean it's not likely to overload. Generally that's when you know maximum possible current a load can draw and have cables can supply that. Logically if a overload can't happen, there's no real need to provide a protective device to prevent it (but normally you'd still have to provide protection from faults (e.g. short-circuits).
You should apply a little care when using that get-out though as some devices can draw a larger current, but less than a typical short circuit current, when certain internal faults occur - say a short part way along a heating element or transformer winding. Often the design prevents that or would produce an earth fault current that an upstream RCD would detect, so would fail safe as far as not being able to overload is concerned, but not always.
We haven't specifically fused sockets for a long time (although it was occasionally done long before the days of 13A plugs) - the wiring to sockets is generally sized according to the protective device supplying it - although there are a few exceptions - such as a spur from a 32A ring supplying a single or double socket where the cable needs only be rated at 20A - that's certainly one example where (ii) applies.
The lack of fuses in plugs, is normally not a BS 7671 matter (as the installation would typically stop at the socket) - but as others have already said the principle for protecting the flex is the same - generally the load would be limited by the appliance. The same logic applies where the fuse is rated higher than the flex's continuous rating (sometimes seen with fridges/freezers were a 13A fuse is fitted with a 0.75mm2 flex - a 3A fuse isn't used as it wouldn't reliably survive the compressor starting currents).
Didn't the OP ask about 433.3.1 (A device for protection against overload need not be provided...) rather than 433.1?
(i) is only needed because 433.2.1 is so badly worded.
(iii) is only for the origin,
so I'm guessing you're thinking about (ii) - characteristics of the load or supply mean it's not likely to overload. Generally that's when you know maximum possible current a load can draw and have cables can supply that. Logically if a overload can't happen, there's no real need to provide a protective device to prevent it (but normally you'd still have to provide protection from faults (e.g. short-circuits).
You should apply a little care when using that get-out though as some devices can draw a larger current, but less than a typical short circuit current, when certain internal faults occur - say a short part way along a heating element or transformer winding. Often the design prevents that or would produce an earth fault current that an upstream RCD would detect, so would fail safe as far as not being able to overload is concerned, but not always.
We haven't specifically fused sockets for a long time (although it was occasionally done long before the days of 13A plugs) - the wiring to sockets is generally sized according to the protective device supplying it - although there are a few exceptions - such as a spur from a 32A ring supplying a single or double socket where the cable needs only be rated at 20A - that's certainly one example where (ii) applies.
The lack of fuses in plugs, is normally not a BS 7671 matter (as the installation would typically stop at the socket) - but as others have already said the principle for protecting the flex is the same - generally the load would be limited by the appliance. The same logic applies where the fuse is rated higher than the flex's continuous rating (sometimes seen with fridges/freezers were a 13A fuse is fitted with a 0.75mm2 flex - a 3A fuse isn't used as it wouldn't reliably survive the compressor starting currents).
