I have never seen any requirement to do so in any Owner's Manual.
As to why I stated not to attempt to shift into gear without either the Propshaft or Driveshaft turning, is due to the design of the Gears and the Clutch Dog. As you have seen when looking at the Parts the Gears have what are Troughs with Stops where the Teeth on the Clutch Dog engage when the Shift Mechanism is operated. When the engine is running, those are Troughs are open a good portion of each evolution of the Gear, and the Dog can engage. However when the gears are not turning, there is the chance the Dog will contact the Stop, and not be able drop into the Trough. With the Dog unable to fully move, that puts very large amount of Stress on the Shift Linkage as you keep on pushing the Shift Lever towards full engagement, so you can operate the throttle linkage. Results can be bent or broken parts in Shift linkage/mechanism. Simply rotating the Prop by hand/foot as you try to shift a non running engine, will expose the Trough.
Some motors will use gears that have Ramps instead of Troughs, Mercury for instance, does so with the Forward Gear, and the Clutch Dog is moved by spring Pressure into gear, not by direct connection to the Linkage. However the Reverse gear is usually a Trough type, so shifting a Merc into reverse while not running requires the spin the prop routine.
