[broadgage]

Very small fuses might spoil in storage due to oxidation of the very fine wire, or they might have been defective in the first place and this not noticed until put to use.

I doubt that 13 amp plug fuses would suffer thus.
Almost certainly the reported failure was due to poor contacts heating up under heavy load. I have observed many very similar failures of fuses/fuse holders in plugs and trailing sockets.

I agree that most designs of 13 amp plug and socket are not suitable for a long hour full load.
This is reflected in appliance designs, very few modern appliances use more than 10 amps other than briefly.
Tumble dryers and space heaters are generally a maximum of 10 amps these days, partly I suspect to avoid warranty claims for melted plus.
Immersion heaters are often a full 13 amps, but SHOULD NOT be connected via 13 amp plugs.
Kettles are often a full 13 amps and are fine in view of the short term use.
SOME washing machines use 13 amps when heating the water, but not for long due to the small water volume used by modern machines.