Because it doesn't smokes in normal operation, under the designed current, of course.
In any case, a fuse would have done a much better job at failing under higher currents than normal.
That doesn't mean the current wasn't limited or limited to the point of failing safely, instead of violently.
It didn't fail safely. That's a massive amount of smoke, and that means heat, and that means something is burning, and that something is the enamel, which is the only isolation of the windings inside the transformer. That amount of smoke can trigger a smoke detector, and with good reason.
Are you doubting the fuse will make a difference?
Fuses are widely used as safety devices their efficacy isn't usually doubted.
Considering the far-fetched examples discussed here, it'd be good to see the actual difference it makes. Not only whether the device fails safely, but also whether a fuse with the wrong current rating saves the device completely.
What "wrong" current rating? This soldering station would likely have a 0.8A to 1A primary fuse, if they bothered to install one. If it's connected to 240v instead of 110v, that means at least twice the normal current, and in practice likely more.
In any case, if the enamel burns before the fuse blows, that sounds like a badly chosen fuse to me. Of course in this case there was no fuse, so it's not surprising that the thing smoked.
I live in a 220v country, and i seen some 110v equipment connected to 220v. And we are talking about the lowest quality chinese computer AT and ATX PSUs with a 220/110v switch here. Of course, they didn't work again without repairs, because the power transistors failed, but nothing smoked as badly as the transformer on the Weller.
I even have a 110v Epson LX-810 lying around that my brother connected without the 220 to 110v transformer, and back in the day i opened it without much hope, but only had to change an internal fuse and it worked again.
Anyways, it would be interesting to check exactly what fuse do reputable soldering stations normally have. If there is a datasheet for it, that's good data to check.