My experience is Rotax engines:
Why, on shut down, would one then put the mags back on?
We follow the procedures as set out by SSD above. One off/on, the other off/on, then both off. Listen for the mag drop.
Engine is now stopped, time for tea and biscuits.
Why would we flip them off and then hope there is enough enertia in the prop to give the required 300rpm so that the mags will allow the engine to fire up again if we flip them on? And then just switch it off?
Rotax's are like car engines, turn them on and turn them off - no running rich or lean etc.
To be frank, mags off engine stops. Quick as that! And the Rotax mags have a safety feature built in so that you need 300rpm on the prop to fire.
Ask anyone with a Rotax 912 - particularly the 912S - and the biggest problem for your engine mounts and sprag clutch is starting in winter and getting the engine to half fire, cough and splutter and not really get going. The kickback on the 912S is a real engine knackerer.
It also can eat engine mounts on C42s, Eurostars, Europas and weightshifts - from personal experience. With 4,000 hours on 912 powered C42s at Strathaven, we have some idea of what is good.
None of the above applies to legacy engines, no idea about 100ll guzzlers!