Here is my take on those Edison fuses,
In all furnace designs if the blower goes out you'd also want to shut off the furnace / turn off the fuel source, (gas / oil valve).
On a new gas/oil furnace there is a 'mother board' and sensors that provides safety controls and the motor is a hi efficiency electronically commutated motor (ECM).
On old furnace designs (but may still be in service) the 'motor overload' is moved exterior to the unit so it can turn the entire furnace off if the motor overloads.
While many appliance small factional HP motors are 'shaded pole' and thus 'impedance protected', I'd say most a older oil/coal/gas furnace blower motors would typically be Permanent Split Capacitor (PSC), and thus *not* impedance protected (I am generalizing)
If the capacitor fails it sits there trying to start but can't due to the failed capacitor.
The windings basically turn into a heating element when there’s no electromagnetic resistance from the rotor spinning.
Without the Edison fuse obviously a 15A inverse time breaker (or fuse) would never trip, much less a 20A, so if sits like that long enough eventually it damages the windings.
Fractional HP PSC Motors have had a temperature overload that melts for a long time (not sure when that was invented), but that is embedded in the windings and not typically user serviceable, and it would not shut off the entire furnace.
So my guess is the Edison fuse is set to trip before the motor overload so the entire furnace / fuel is cut off