I imagine this set was originally conceived out of necessity for "The Doomsday Machine," since they used a portion of the standing Enterprise interior sets for the Constellation interiors, temporarily 'damaging' the sets for the latter by spray painting on fire damage and adding a bevy of bent conduits. A second control room was needed as they couldn't damage the bridge set--the majority of the scenes on the Enterprise were shot on there.
Interestingly, viewers first saw this set in "The Changeling," which was broadcast before but shot two weeks after the first episode where the ACR was shot on, "The Doomsday Machine." They had to damage it before they first shot on it! That also explains why the set is more ornately decorated in "The Changeling," with a computer access for Spock and additional computers in the engineers section.
I covered these points in the article.