Keeping one's finger off of the trigger is not unachievable; indeed, every infantry organisations instils that from the beginning in its riflemen. It's really Not That Hard. And indeed, one sees that negligent discharges are actually pretty rare, even in war zones.
That approach quickly plateaus. Then more discipline harms improvement because people just start covering up mistakes to avoid punishment. In addition to being covered in the book on air safety I already mentioned, your "beatings will continue" theory is basically why Detroit spent decades trying and failing to make cars as reliable as Toyota's. This was true even when Toyota went to great lengths to teach GM how to do it.
That experience was covered engagingly in This American Life's episode NUMMI: