Seems to me that always leaving the fuel ON was setting a trap, simply because pilots might then get out of the habit of checking the selector's position.
I know of one company (rotary wing) who for their own reasons decided on a policy (contrary to the RFM) to have the electric LP fuel cock switches permanently left at the ON position. Probably because on the aircraft type involved, the number two / right hand switch is hidden under the collective lever and there is no warning, other than the position of the switch itself, to indicate that the airframe fuel system is OFF. The fuel pump pressure check is done after start.
It's not unheard of for a pilot to get an engine going only for it to stop when it runs out of fuel after a minute or so. The company in question then had the switches modified by fitting a copper "tell tale" wire. That would certainly prevent an engine from failing after start up.
However, a pilot later had cause to switch the fuel OFF but one of the cocks wouldn't motor closed; probably due to lack of regular movement of the valve mechanism. Not good because one of the immediate actions for an engine failure or engine fire is to switch off / close the valve....