The TVTropes Trope Finder is where you can come to ask questions like "Do we have this one?" and "What's the trope about...?" Trying to rediscover a long lost show or other medium but need a little help? Head to Media Finder and try your luck there. Want to propose a new trope? You should be over at You Know, That Thing Where.
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[Insert clever saying here]
Erm... soldiers are supposed to do that, aren't they?
^ I'm looking for when it is exaggerated
[Insert clever saying here]
The soldiers at the bottom of the chain of command are supposed to follow lawful orders. That's a baseline. There may be an association with Just Following Orders if the officer wants exclusively soldiers who will say "I was just following orders" even if they're commanded to perform atrocities, as opposed to soldiers who will hesitate on ethical grounds. That might count as an Invoked Trope or Exploited Trope — the officer set up the trope to happen by being very selective about his soldiers.
At the higher up levels, like a general who surrounds himself with sycophants and wants colonels and majors who are yes-men, it sounds more like The Generalissimo. It doesn't quite fit your question, I admit.
Edited by KD
Soldiers at the Rear covers super active soldiers, though not necessarily soldiers who obey every single command.
Silver and gold, silver and gold
Do we have a trope where soldiers who obey every command from their military officer are seen in-universe as the best type of soldier? Think this scene from Forrest Gump: https://www.youtube.com/watch?v=a4gCt1rUEpE