As a diver and now more a boathandler for divers I have only ever operated the "engine on all day" dogma without question, this thread is interesting, as mentioned a boathandler will routinely leave the engine on and disconnect from the killcord. I have also accidentally smashed the detent/throttle lock it took a bit of doing, however as a guestimate a divers backside sitting on it if they overbalance should suffice.
Interestingly when we bought our boat surface mounted throttles were rejected (even though I did try and point out they were arguably safer than side mount) on the grounds of accidental knocking into gear, clearly no one thought of turning the engine off at this point. During this years boat handling I have had 2 ocasions when people have either moved past the throttle or grabbed the throttle accidentaly whilst under way.
The only other argument for engine on all the time might be being ready to react to an emergency imediately, though there are other factors and issues that could lose you the 3 to 4 seconds an engine start takes. I will be thinking carefully about this as our boat briefing needs an enema.
New boat is here, very happy!