Apart from scheduling problems, I'm pretty sure it would be illegal for POTUS to personally kill someone in general (apart from self defense, etc.) and in the specific case of military law, there's still a judicial process involved.

From a game-theoretic standpoint, what does it matter whose job it is to pull the trigger, to the person considering disobedience? The credible threat is what distinguishes between manipulation and coercion, regardless of where that potential violence is being stored.