Here's the sticker: SpaceX (or whoever) is going to make a profit by selling hardware to the government, not by going into space themselves. It's a fine distinction, but the key difference is that the second the government closes their purse the space "market" collapses. In truth it's still a government program run (at a massive loss) with taxpayer bucks.
Very similar to early air travel. Took government mail contracts to make it viable/profitable.