What you're claiming here is that Musk can allocate capital better than a government, right? That leaving the money in his hands was better than taxing it and spending it on government projects? (note that all three of SpaceX, Tesla and Solar City received substantial amounts of funding from the US government (directly or indirectly) and would likely not be viable without it, even leaving aside all the USG-funded basic research that was necessary to make them possible in the first place).
Even if that's true for Musk specifically (which I doubt), is it true on average? How efficient is the average billionaire at using their money for social good? You gloss over a lot with "While not always the case" - how does the average return to society on a private capital investment compare with a public capital investment?