I'm not keen on reviving ancient electrical equipment. The past was not good at electrical insulation and heat-proofing materials. Many improvements made over the years.
I wonder if the practical experience of mechanical engineers distorts their judgement. A well-maintained lightly loaded Myford lathe could be mechanically as good as new. Not so its electrics! 1948 insulation, switches, and capacitors etc do not age well. Fortunately, not difficult to replace and improve on the original electrics of a Myford, though bigger 3-phase machines with no wiring diagrams can be a challenge! You can even CNC them.
Frankly, I wouldn't fix an old electric soldering iron. It's hardly mechanical at all, and other rules apply. If one part has failed, chances are the rest of the poor thing is on the way out. Might even be a shock hazard. Think how long manufacturers expect a tool to last in service when new. Probably between 3 and 7 years in a busy workshop, perhaps less. An electric iron was unlikely to have been guaranteed for more than a year.
As always, if the hobby is restoring old gear, then go for it. Just be aware that restoring isn't the same as bodging clapped out junk in hope of saving a few precious pennies.
Dave