The first problem with the libertarian argument is that free markets exploit only that which is profitable. Discovering that which is profitable is often a thing done by or for governments. If you look at the history of innovation over the past hundred years, almost all of it would have been impossible without the direct involvement of government. The computer was developed for the defense industry, as were rockets, jet propulsion, modern nuclear physics, refrigeration, microwaves, radio, the list goes on and on.
Lately the profit motive behind going to space has been more or less limited to tourism. A visit to the moon by NASA, especially an extended manned one with the intention of exploiting the moon's natural resources and discovering the problems of long-term hostile-environment extraplanetary colonization could provide the very sort of research that would create a profit motive for private industry to exploit the moon.
The second problem with the libertarian argument is that the companies developing these technologies already are private industry, they are merely funded by the government.
The third problem is the cost. If you compare government spending in any given year, 3bn is a drop in the bucket, but it's a drop in the bucket that could result in MEN WALKING ON THE FREAKIN' MOON. What part about MEN WALKING ON THE MOON did you miss?