I don't think aerospace is a good example of efficiency in the private sector. Lockheed Martin did the F-35 and it's main competition in the US is Boeing...
I'm not an expert but from my friends in the industry (including multiple at Lockheed and Boeing), it's definitely not a story about how good and efficient the private sector is. Boeing especially sounds like it's been a real mess with a lot of project management issues.
Those traditional prime contractors are basically part of the govt bureaucracy with how they operate. SpaceX and Anduril are good counterpoints.