Note that when surnames came into existence, they were intended to distinguish their bearers from other people in the local area with the same first name. There's no point being called John English if you live in England and everyone else in your village whose name is John is also English, which is why the surnames English and England (and variants like Inglis) are more common in Scotland than in England.
Similarly, Smith is a common surname because smiths, while relatively common, were rare enough that a given community was unlikely to have two with the same first name. There were almost certainly more shepherds than smiths in England when surnames started becoming heritable, but the surname Shepherd is less common.
Ive heard the possibly apocryphal reason for this is that invading armies would kill or appropriate workers in other professions but keep around the trained blacksmiths working the forge and producing weapons and tools for war. Smiths survived the waves of conquerors.
There were technically invasion attempts up until the 18th century, but even discarding most of those as insignificant, we can hardly neglect the War of the Roses and Henry Tudor's (successful) invasion in 1485...
I have that surname but not for the reason that a blacksmith was in my family. My great grandparents took the name Smith at Ellis Island to Americanize themselves. I suspect this backstory is probably quite common in the US, especially amongst Irish and Italian immigrants in the late 18 to early 1900's.
Probably not; the odds are very high that the name "Smith" (or any analogue like "Kuznets") originally refers to a blacksmith. Most metalwork is ironwork.
Similarly, Smith is a common surname because smiths, while relatively common, were rare enough that a given community was unlikely to have two with the same first name. There were almost certainly more shepherds than smiths in England when surnames started becoming heritable, but the surname Shepherd is less common.