I've been trying to set up a practical experiment, as it's clear it will be an endless discussion otherwise. Unfortunately, very few donations have materialized. It's a bit disappointing that some people making adamant claims aren't as keen on having them tested.
I am most curious as to what point (as the input voltage is raised,) transformers like this typically start to saturate and dissipate significant heat in the primary winding itself. There will be a point at which the primary is dissipating virtually all the current that the whole device is supposed to be able to draw, hence will not blow a primary fuse because it is still within the ratings, but will be coming out as primary heating, where the primary should normally dissipate very little energy in regular operation.
The primary saturated and ran well beyond 4 times normal power dissipation, and then likely went into accelerated melt down as the enamel was burnt off and the primary turns shorted.
The primary normally dissipates
very little current. Most of the energy is passed to the secondary and whatever is connected, not dissipated in the primary. The "4 times normal" is effectively nonsense when it comes to primary power dissipation.
Most transformers will have some point where the input voltage, frequency and waveshape makes the primary dissipate
far too much power for the transformer to survive but is still well within the total input current range that the devices would be fused for.
People are essentially arguing, therefore, that not only should a primary fuse be mandatory but also a mandatory thermal fuse inside the transformer. Those ones that once they decide to open (often
not due to a fault) your transformer is usually junk because the thermal fuse is buried deep within the windings making repair impractical.