NASA does work with private industry and educational establishments. In fact Lockheed Martin manufactured many components on the Space Shuttle and will be building its replacement as well. http://www.npr.org/templates/story/story.php?storyId=5748366
I don't share your faith that this is a recipe for efficiency, as both Boeing and Lockheed regularly lobby congress for wasteful spending (however, usually for defense, not NASA).
I think the gap between your perspectives comes from the existence of lobbying and the bid process not being open. Further, there is less competition because the previous control over the entire industry that NASA enjoyed prevented many possible competitors to LM or Boeing from getting off the ground.
Of course there is a wide array of subcontractors involved in NASA projects. I don't think anyone who accuses NASA of being inefficient thinks that NASA workers do all the manufacturing, etc.
I don't share your faith that this is a recipe for efficiency, as both Boeing and Lockheed regularly lobby congress for wasteful spending (however, usually for defense, not NASA).