I don't know why they used them in the past I never saw them used on furnaces around here.
All furnaces now require a dedicated branch circuit and the blower motors have thermal protection.
Thats interesting you never saw them.
I *think* the early internal motor thermal protectors were a one and done, not resettable / replacable, so you'd want that Edison fuse to be a very exact amprage (like 6.25) amps so you blow the fuse with a locked rotor not melt the thermal link in the winding.
On those early systems I suspect they wanted to shut fuel source down if the motor locked up, so another reason to use the external fuse.
I think today's 'forced air' blower fans in furnaces came out around 1935, before that for ducted air type furnaces were not that good, it was natural convection only.
It seems in northern climates boilers and a hydronic hot water or steam to radiators systems were more popular until A/C came down in price and people wanted a dual system, hence central air took over, it cools in the summer heats in the winter, so many homes may have been converted from hydronic boilers to forced air. Boiler systems would also want to cut the fuel on motor overload so I'd guess external fuse, but perhaps they used relays?
It was probably not uncommon to see Coal furnaces that had been converted to oil burning in service until recently in your part of the country?
Here in PNW it was logging / lumber mills everywhere and people actually had sawdust furnaces, not that much different than a pellet stove.