That may be so, but I think it would explain only why Trump doesn't engage in war or personally kill, not why he doesn't start wars or order others to kill for him.

Plenty of psychopathic rulers in the past have been too pampered and decadent to get their hands dirty or to risk their person by directly facing their enemies. They "lead from behind," satisfying their narcissistic whims by indirectly conquering territory and crushing weak populations via their armies. Trump's personal cowardice wouldn't explain why he doesn't start wars from the safety of the Oval Office.