Government funded programs in the US and Russia took care of a lot of the basic science companies like SpaceX rely upon. It is unlikely that a commercial venture would have been able to attract or afford the depth of engineering talent that got the Russians the MIR Space Station or the Americans the moon landing. They are treading the path blazed by government funded research. That said, there is no reason a hybrid model (government + private sector) could not work well.
Most basic research is government funded - and private companies using that basic research is exactly the way things are intended to be. Open-source the lot of it!