But... that's the model of the US space program from the get go. We're just trading one private company for another. Apollo 11 was contracted out to Boeing, Rockwell, and Grumman. The Space Shuttle was the United Space Alliance (Rockwell / Lockheed Martin), the engines were made by Rocketdyne...

The only change right now is that NASA is no longer the only party designing missions, because entities such as SpaceX have enough integrated expertise to run their own show start to finish.

It's also the most successful space program in the world, so what's the benchmark we're comparing it to? The failings of the US space program had relatively little to do with private contractors, and a lot to do with politics and the voting public not liking risk.