Re “professional saw sharpening shops”
  Most of the busy shops of the last century had Foley Saw Filing machines
as well as Foley re-Toothers that could punch in new saw teeth.  I’ve had
bits and bobs or old machines in the past but the main drawback is that the
template bars are almost always MIA when these machines were sold by the
estate ( often only having the last used bar mounted in the machine when it
was sold.). There’s an active group around that provides support for people
interested in these old machines and someone was machining new template
bars (or whatever they were called) for restoration projects.  I doubt that
many saw shops spent much time hand filing anything.
 Cheers from Waterloo
Claudio