It's not impossible, obviously, but while it was natural for steam-engines to appear when they did, there is no good reason to expect an essentially arbitrary w

It's not impossible, obviously, but while it was natural for steam-engines to appear when they did, there is no good reason to expect an essentially arbitrary word to be synthesised many times nearly simultaneously. A weaker version of your hypothesis, whereby the word was synthesised once but reinforced by similar phrases or folk etymologies (leading to the current confusion) is much more plausible, however.