This is exactly what the TNG episode “Lower Decks” was about. It was actually super powerful as a representation of how the decisions made by the captain and bridge officers had a profound impact on the lives of the ensigns (NCOs didn’t seem to be mentioned), without them knowing what’s going on.
The show lower decks was obviously inspired by that specific episode, but definitely lost that serious tone and lack of visibility into the politics/big picture that the captain dealt with.
And honestly I think star trek forgot that NCOs existed and just kept remembering it each time Chief O’Brien had a major episode and his rank came up.