This sounds unnecessarily nit-picky, especially when "they dropped a red-hot sword on themselves" is both "not authoritative" and it's kind of ridiculous to expect that this would happen
so often that myths would be built around it--and that
only the resultant limp would be build around it and not the clumsiness.
With all respect, wikipedia saying his disability is "taken by some" is not authoritative.
Especially when the same wikipedia article notes that the source of Hephaestus' disability is explicitly given in the myths - he is either born that way, or Zeus injures him for trying to protect Hera from his advances. Similarly with Vulcan - he's an ugly baby, so Juno pitches him off Olympus, and he breaks his leg in the fall.
OK, you do know that these origin stories are made up by human storytellers, right? There wasn't some documentary crew up on Mount Olympus actually recording everything. The stories are supposed to be fantastical and contain larger-than-life individuals and events.
Bronzesmiths had injuries and malformations often enough that this became memetic, in the original meaning of the word meme: information that is passed on from person to person.
The early storytellers knew the meme. They
may or may not have known its origins. Maybe they knew enough about smithing to know that something about it injured smiths and/or smiths were extraordinarily clumsy. Maybe, being storytellers or priests, they didn't have much to do with the people who did physical labor and therefore had no idea why.
So here comes a story about Hephaestus, and he
clearly has to be disabled. How? Well, they
could use something boring and human like weird chronic diseases or accidental injuries,
or they could use the idea that had thrown from the heavens or injured by a god.
With respect, this assertion that the Bronze Age people "wouldn't care" is pure supposition on your part, with no supporting evidence.
The people of the Bronze Age were not stupid. They could tell the difference between an injury, and a disability that develops over time. If they could tell the difference why would they not care about that difference? Why wouldn't that difference be in the myths that explain their world?
I didn't say they were stupid. I said they wouldn't care because that bit of knowledge isn't needed when it comes to telling a story. It's not like these myths were written with scientific or medical realism in mind.
(Although they
did use arsenic in their bronzemaking--admittedly, this was a millennia or so before it was commonly known to be poisoning--so yes, I think that maybe
no, they didn't know that some of the materials they used had toxic effects. Especially since it
can cause neuropathies which can make other injuries easier to obtain and therefore the exact cause of those injuries would be harder to pinpoint--if someone broke a leg, how exactly would they know if it was because they fell or because they were suffering from bone degradation that caused the bone to be weak enough to break.)
One would think that if they knew the difference enough to put it in their myths, the stories wouldn't have to say "Hephaestus got thrown from Mount Olympus" and instead would say "Hephaestus dropped a red-hot robot on his foot and it burned clean off."