I don't know why the changes have happened, but I'm terriffically sensitive to checking the governor after a minor distraction cost me £1000 insurance excess.
My understanding why RHC want governor on below 80% is to check for full and correct operation throughout the whole governed range. The checklists in the aircraft I fly have been amended - with CAA approval - to "increase to 100% RPM, governor on" and there's an optional throttle wiggle to test operation from about 97 to 105%.
As for leaving the governor on at shutdown - why ? Makes no sense to me. Is there any parallel with the turbine world ?