Your theory rings true. Maybe he/his advisors also felt that the mispronunciation also made him seem more like the an “outsider,” more like the “underserved,” more like someone with only a basic reading level, more like the kind of people he was pretending to serve. The one thing the image too the chance of excluding was anyone who had served or had had family in the military.
That’s a good reading of the situation. Obama knows he’s not popular with those who serve, have served or have family serving. Alienating them still further costs him little or nothing. Plus he really is petty and childish enough to enjoy giving insult to those he dislikes. The middle-finger he gave to Hillary on one occasion, and to others [look up ‘Obama gives middle finger’ in images—he does it quite a bit] is juvenile beyond belief. The same person who engages in this infantile behavior wd certainly mispronounce corps if he thought it wd serve his purpose. It’s repulsive.