Why all public goods are not produced in the public sector?

Think about it. What makes a good public sector is not its production, but who is willing to pay for it, given the free rider problem

http://en.wikipedia.org/wiki/Public_good

http://en.wikipedia.org/wiki/Free_rider_problem

The government has no expertise in producing airplanes, and while Lockheed-Martin has expertise, it has no private customers that would buy fighters, but if the U.S. government were to place an order, Lockheed-Martin would be happy to build them.

Similarly for Rockwell International and the first generation of NAVSTAR (GPS) satellites, civil engineering specialists (Bechtel, Parsons Brinckerhoff, etc.) and major infrastructure projects here on Earth (bridges, tunnels, interstates, etc.)

Similarly for the fireworks paid for by governments but actually created by private pyrotechnical firms.