Such stuff has to be tested to achieve CE / UL whatever.
I guess it has been tested for secondary shorts and overload, that's the way the secondary fuse and polyswitch creeped in. From my experience with testing according to standards (whatever standard applies) today, everyone does test exactly what the standard and auditor requires, but nothing more. So, in case the standard didn't require testing a 120V unit at 240V mains, no one would have tested that.
Here, where I'm working, one can see strange things happen.
For example, someone designs a flyback converter for a 24V to 12V (plus several auxiliary voltages) conversion, it's a flyback because isolation is required and it's always been a flyback for that kind of application.
Now, some testing happens. Someone else discovers, the transformer runs hot if one of the auxiliary outputs is shorted or overloaded. The flyback isn't designed to go into hiccup mode then (for unknown reason, or maybe just ignorance), so the transformer runs too hot. Now an protection circuit gets added to each auxiliary output that shuts down the converter in case of overload or short. Test passed then, everything is fine, converter board costs more than planned - no one cares now. Only the orignal designer was pushed to reduce cost, not the other ones that added the protection circuit.
This converter circuit get reused once. Someone discovered the controller doesn't limit the output power in case of the main output is overloaded. By chance, the original designer was asked and added a clever workaround at minimal cost. Test passed, everything is fine.
Not this converter, including all the protection circuitry plus the original designers clever workaround gets reused again, by some new designer who isn't familiar with the original designers intents. The circuit just gets copied, for some reason a new transformer is designed (smaller than the orginal one), and one auxiliary supply is removed. So the removal of this auxiliary output also removed the snubber circuit (one more clever idea of the original designer was to use the primary snubber as an auxiliary output) - a new snubber circuit is added to make it work again. This circuit gets tested and someone else discovers the primary controller doesn't shut down it the main output is overloaded. The original designers clever workaround is still there but doesn't work here because of the new transformer or whatever. The one who is testing doesn't know about the clever workaround anyway, so he adds another (complex looking) protection circuitry that isn't working on the first try, so a respin is needed. Finally test passed, everything is fine.
Result: a very compicated looking schematic of an rather simply flyback supply. Best part still to follow: At some point the requirement for isolation was dropped, input and output GND were bonded together and the whole thing could have been done with a way more simpler buck regulator.
So, I'm really not surprised at all by the missing primary fuse and the bullshit polyfuse / fuse combination on the secondary with this transformer.