Or, convince me that without the initial public investment, any private company would have done the basic research required to send the first satellite into space.
It's not my job to convince you that the private sector would have magically brought about the space age without government intervention, because that isn't what I'm arguing in the first place. Sure, there are lots of examples of technology invented (or aggressively developed) by governments - pretty much anything with military utility, in particular, which includes computers, the Internet, radar, jet engines, and especially anything to do with space. The key detail here is that most of these eventually developed independently and became consumer technologies, rather that continuing to be government programs indefinitely. Yes, this means that private companies eventually get rich because of public sector investment; it's also what makes it possible for us to be having this argument right now. Without Colossus or ENIAC, there would be no iPhone, but if computers and the Internet had been managed like manned spaceflight was, there wouldn't be an iPhone either.
The other important and essential outcome is that it needs to be not just profitable but sustainable; continuing to pour billions of taxpayer dollars into something that never gets cheaper is anything but. SpaceX has already made unmanned launches cheaper; the shuttle program lasted for three decades and it was still hideously expensive when it ended.
The reason this is exciting news is that it's real progress towards making manned space travel yet another consumer technology. Maybe it won't work, or maybe it will only ever be affordable by large companies and the rich; I don't expect to be personally taking any rocket trips before I die. But the same could have been (and probably was) said about airplanes a century ago, and I was never going to be able to ride on the space shuttle either. At least someone is trying to change the way things are done, and doing a decent job of it so far. So what if SpaceX piggybacking off years of government investment? If their business model works, at least we won't have to continue wasting money on something that should have been commodified decades ago, and NASA will be able to focus on science and basic research (and stretch their budget further). Everyone wins.