In terms of innovation, the private sector is not suited to long term projects. This is because corporations are based on quarterly reporting. If a project takes 20 years to complete, or even just to show some progress, that project is less likely to receive continual funding.
You can't do long term space exploration on for-profit means alone or folks will run just like they did from the Air Taxi idea--not because it was a bad idea necessarily. F-35 might wind up being a pretty good fighter. Venture vultures are drawn to computers because computer companies have less up-front costs than aviation. This serves as a brain drain to the point that we have profits without products.
Some things are more important than mere ferengi profit motive. Spaceflight is to be compared with the eradication of polio--it is the right thing to do--profits be damned.