But far more importantly, you have not argued why industrializing the moon is a good idea in the first place. I wholeheartedly agree with the idea that operations on Mars will never turn a profit for Earth, but that hardly supports your point. Putting factories on the moon might make (marginally) less losses than putting factories on Mars, but so what, there is always the option to stay home and make no loss.
Industrializing space is desirable because industrializing Earth has had a number of negative side effects on the biosphere, so moving production outside the biosphere would be a positive development. My argument is that the option of staying home is clearly economically preferable for now, and will be unless we see major cost reductions in space technology.
Whether SpaceX and other launch vehicle organizations can reach the Level 2 threshold you describe remains to be seen, and LVs are only part of the pricetag. Materials, equipment, and labor represent a large segment of space mission cost, and unless we can also drive those down by similar degrees do the economics of colonization start making sense.
Note, too, that ΔV is non-trivial, even when we start getting to high specific-impulse technologies.
This doesn't really address my basic question, which is why the government or private sector would want to sink the necessary funds into setting up such a project.
The important question isn't the desirability of going, but the costs of getting there. Space tourism at it currently stands means paying at least $20 million, going through a condensed astronaut training program (and passing), and then spending around ten days in low Earth orbit. Unsurprisingly, only a handful of extremely rich individuals have paid that much.
Lunar surface tourism would be considerably more expensive. Building a small space station in low Earth orbit where tourists can experience weightlessness for an extended period would probably pay off better. Right now, we're still waiting for suborbital hops.
There's another cost, as well: the same age that makes low gravity attractive also makes a rocket launches precarious. (Sure, if we had a space elevator, that wouldn't matter, but if we had the technology and funding to build a space elevator I wouldn't have written this post.) Not coincidentally, a lot of astronauts retire in their 50s or early 60s. I don't know how much this would depress the demand, but it would certainly depress it some, and also raise the legal and operational costs to prevent liability.
Tourism might be a big market once the infrastructure is there, but I'm not sure how well it will serve to fund the infrastructure and technology development itself. As with the other potential markets I mentioned, whether we would like to do it has relatively little bearing on whether there's sufficient willingness-to-pay such that we actually can do it.