Now we get into considering things like 'duty cycle' etc.
Yes, the output transformers for 'Audio' usage DO pass through all those wave forms. BUT it is with vastly over designed transformers. Both electronically, and physically. Things like the 'molecular structure' of the 'core iron' make a big difference in operation (or lack thereof).
'Horizontal Output' for a TV (& VDTs) --- (Also the same circuitry provides the HV for the picture tube.) Designed for a very specific and stable set of conditions. Doesn't use the same sort of 'iron' used in60cycle AC power transformers. (Gee, even the NAVY [& AF] changed the transformer construction rules [back in the WW II days] when they used 400 cycle AC for power on ships & Planes [they wanted the weight savings])
Your 'Resistance Soldering Rig' You most likely have a 'foot/ knee/ thumb' switch in the primary of the final transformer, (or maybe before the 'dimmer'). In any of these cases, the loaded 'duty cycle' for the 'dimmer' is probably less than 20% over a 5 minute period. The output transformer is probably capable of withstanding a 'dead short' with110VAC on the primary for a couple of minutes without failure, so you just haven't gotten the stress levels high enough yet to see the 'bad things' happen. But that doesn't mean that they can't happen.
When offering comments on the NET, I always try and allow for a "Thumbs" type to be reading and absorbing the information.