Let's be careful, if that's possible with all the flames here.
There are
component-level certifications for a power transformer, like UL 1411, UL 506, CSA 22.2 No.66 and IEC 61558. We don't know this transformer's approvals.
There are
product-level safety standards for soldering irons, audio-, radio-, and television-type appliances, IT equipment etc.
There are regional differences in safety standards between North America, Australia and Europe as well for the component's and the product itself.
It makes a complicated soup.
Weller safety cert. for Europe is IEC 60335, and the 240VAC transformer pic
https://www.eevblog.com/forum/blog/eevblog-1160-weller-responds/msg2051086/#msg2051086 shows a third bobbin lead, surely a thermal fuse is in there. 60335 does not specify a mains fuse but calls 61558 for the transformer's requirements.
Weller safety cert. for North America is UL 499. A different standard with different requirements, although the confusion around other soldering stations incorporating a primary fuse begs the question of WTF. UL 499 seems for higher power heaters and the mains breaker is the protective element.
At the 80VA power level, it is not an "energy-limited" transformer (Class 2) or "fail-safe".
This was not a "normal use" scenario as defined in the safety standards - but it did flush out an error in the product's safety.
Is there a safety hazard running it off 120VAC? Of course. I've seen three power transformer fires in electronics gear, quite a mess of smoke, soot and carbon.
Notice
other safety standards IEC 60950 and 61010 require a fuse (DUH!) and (torture) load test a transformer for "maximum heating effect" limited by the fuse if there is one:
IEC 61010
9.6 Overcurrent protection
9.6.1 General
"Equipment intended to be energized from a MAINS supply
shall be protected by fuses, circuit-breakers, thermal cut-outs, impedance limiting circuits or similar means, to provide protection against excessive current being drawn from the MAINS in case of a fault in the equipment."
4.4.2.7 MAINS transformers
4.4.2.7.1 General
"The secondary windings of MAINS transformers shall be short-circuited as specified in 4.4.2.7.2, and overloaded as specified in 4.4.2.7.3.
4.4.2.7.3 Overload
Each untapped output winding, and each section of a tapped output winding, is overloaded in turn one at a time. The other windings are loaded or not loaded, whichever load condition of NORMAL USE is less favourable. If any overloads arise from testing in the fault conditions of 4.4, secondary windings shall be subjected to those overloads.
Overloading is carried out by connecting a variable resistor across the winding. The resistor is adjusted as quickly as possible and readjusted, if necessary, after 1 min to maintain the applicable overload. No further readjustments are then permitted. If overcurrent protection is provided by a current-breaking device, the overload test current is the maximum current which the overcurrent protection device is just capable of passing for
1h. Before the test, the device is replaced by a link with negligible impedance. If this value cannot be derived from the specification, it is to be established by test.
For equipment in which the output voltage is designed to collapse when a specified overload current is reached, the overload is slowly increased to a point just before the point which causes the output voltage to collapse.
In all other cases,
the loading is the maximum power output obtainable from the transformer. Transformers with overtemperature protection which meets the requirements of 14.3 during the short-circuit test of 4.4.2.7.2 need not be subjected to overload tests. "
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In all likelyhood, UL 499 has been wrongly interpreted/assessed or is simply antique.
A modern safety standard like 61010 and 60950 requires a fuse, which is what I go by.