The big cost of space flight is really nothing to do with the fuel, although the fuel cost is not nothing. The big cost is the sheer complexity of the whole operation, mainly due to the fact there is very little margin for error between getting to orbit and failing catastrophically.
Space tourism may seem like a trivial use of space flight but actually makes sense, given you can get millions for transporting a few kg of people. Any other use like space solar, mining asteroids etc, requires a massive infrastructure cost.
Musk is maybe slightly crazy, but also has a rare combination of ideological drive, technical ability and business acumen, so if anyone can pull it off, he might actually do it. Certainly, waiting for the govt to pay for missions like established players do (Boeing et al) won't get us far. Don't believe the timescales though, not that it really matters when. Colonizing the galaxy is pretty long term plan.