It is interesting to see imagine the alternative scenario if exploration had been funded primarily by governments. To add further matter to your point, if you consider the expansion into the new world and things like the European expansion into Asia, it is often pioneered by trade. The modern equivalent is private enterprise of course. Historically it is the way that society has seemed to lead to.
So then what is the solution to our exploration of space? Leave the role of space exploration solely to private enterprise or still fund things like NASA? If private enterprise is left as the only bastion of expansion will we still see growth in the area? Space is quite rich in resources that are just waiting for exploitation such as mining, and information systems are more and more important in this age. We've seen increasing private involvement in satellites and further systems will evolve. Yes there are groups like the good ol' space elevator people and if you remember back a few years, the Mars Society (if I remember correctly). They were a group of engineers who developed and proved a cheap, workable system to send manned missions to Mars.
Sadly as we're can all attest to currently, we are lacking our shiny jetpacks and Moon Condos. So clearly the private sector alone cannot be relied on.
What is the best solution then? A synthesis of both as we currently have? The decline in exploration we're currently seeing clearly attests that the status quo is not going to achieve the same levels as desired. Then that leaves increased government funding, which without a clear gain taxpayers are unwilling to support. This is further compounded by issues of safety causing public concern about safety. Interestingly enough if tax payers were not paying for the attempts, I wonder if public outcry to tragedies in space would be on the same level?
In other words clear progress into space is a very difficult problem to approach, and without full support of both private and government we're not going to see any substantial gains made. If the Cold War was good for one thing, it was the Space Race. I do not see anything short of that, or a similar thing happening between rival companies leading to rapid expansion into space.