One more level of complication - well intended as it is = one or more failure modes that could affect propulsion.
If, as the previous poster suggested, it's startup that's to be inhibited with the cowls unlocked, then you won't get as far as having any propulsion to affect.
And anyway the AAIB's recommendation isn't for that, it's for an unlatched condition warning system, not one that commands an engine to shut down.