No, seriously, you're putting forward some very fanciful and hypothetical instances which are fantastic in the extreme.
Besides, a hangman's motto would be much the same as the misrepresented squaddies you mention, i.e.
"Ours is not to reason why."
You're trying to equate two extreme professions to mundane ones like, and no offence meant, a bank clerk, a shop assistant, a bus driver etc etc.
You wouldn't last 5 minutes as a hangman or a squaddie under fire if you decided to stop and have an ideological conflab about why you should be doing what you are.
You'd simply be drummed out and replaced by anyone willing to do the job properly.