... Could someone do an actual experiment to test the assumption that a fuse would help? ...
Measured a 120VAC 60Hz transformer to 190VAC with no load. Past 150VAC it gets very loud.
It is an older Hammond (pre-china) 167M25 rated 25.2VAC 3A 75VA, similar in power to the Weller part but a more conservative build. Primary is 4R 0.77H and secondary 0.3R 50mH.
True input power is about 5W 115VAC going to 90W at 190VAC. Effective turns-ratio did not sag as I expected. I got 42VAC out at 190VAC in, I thought it would eventually clip.
You can see primary current skyrockets from 0.25A at 120VAC, the up to 4A at 190VAC. To 240VAC... I did not release the magic smoke. So a fuse would cover long-term primary overvoltage, a thermal fuse as well with that much heat dissipated in the primary it's heating up.
edit: added 60Hz