If there's a reason to go anywhere, private companies will make it happen cheaper, more efficiently, and faster, than any government agency could.
The only reason for getting to the moon in the late 60's was political. We needed to show the world that our Republic was better than Communism. It made sense for our government to pour the amount of money into the space race in order to win. It doesn't make any sense to spend that kind of money to go back.
However, there ARE good reasons to go back if we can do it cheaper than the government would do it. And companies similar to SpaceX will get us there when it becomes profitable to do so.
The idea that private companies are
individually more efficient than government agencies is pretty dubious. Arguing this point will be less rewarding that trying to argue the definition of "benefit" -- unless you are arguing with someone comfortable with terms like "stochastic frontier modeling" and "data envelopment analysis".
I could offer that I have worked as some kind of manager or technical lead for some very profitable companies -- and that in those roles I observed very little that could be mistaken for rational decision making or well-executed plans to improve efficiency at any level of operations. But anecdotal evidence, especially in the negative (absence of evidence is not evidence of absence), is of little value.
So I will just ask if you count
all of the failed ventures -- the companies that didn't get the contract to launch the satellite or build the moon base -- when estimating the cost-effectiveness of privatizing space exploration? Those companies will have consumed materiel, and spent money on wages and salaries and benefits. Those companies will have employed workers who were pushed to do more with less. That productivity, those expenses, will go to
exactly the same place that alleged government waste goes.
And there is the fact that the profit motive inclines us to ever quicker returns, emphasizing the short-term gain, low hanging fruit, over long term planning. Corporations do not plan for generations. The folks on the BOD will not be expected to think of any posterity but their own. In fact, corporations in the US might decide that SEC regulations prohibit any actions which reduce share-holder value in the short-term in service of a long-term project, no matter the prosocial returns on long-term planning.
As for why we went to the moon -- the Cold War certainly had something to do with it. The promise made by JFK to do it within a decade, and the fact that he was not available to backtrack or apologize if we didn't rise to that challenge, certainly provided political will to do it quickly. But -- in my opinion -- the rationale President Kennedy gave for going
at all is valid, and holds equally well as an argument for going to Mars, or to Titan, or doing anything on the high frontier (to coin a phrase).