F gear has an overrun clutch whose purpose is to allow the prop to "free wheel" when the throttle is reduced....like when you are slowing down and coming off plane. If it weren't for that the prop would be locked to the crankshaft and when the RPMs went to idle say from WOT, the prop would too. So now you would have a brake for a prop rather than a propulsion unit....guess where your teeth would embed if you had a windshield.......
With the engine off, if you shift to F gear and using you hand, rotate the prop clockwise looking from the rear, you will see it move in and out the distance you mentioned and that is the "clutch dog" on the prop shaft moving over the "sawtoothed" shape of F gear.