Does a moon base help? And if it's mining for minerals, is it economically a viable plan?
The science is mostly geology and astronomy --- the moon is a great place for observatories --- but mainly it's engineering and life sciences; the moon makes a great place to learn about how to solve the kinds of problems that you have to solve when living somewhere like the moon. Which sounds tautological, but it's all stuff that we have no idea about and the moon, being on Earth's doorstep, as a good place to start.
Much further down the line, mineral exploitation. Trying to establish a proper presence in space by hauling everything out of Earth's gravity well is ludicrous, and the moon's the obvious place to go for resources. But that's much further down the line; we need to have people living on a regular basis on the moon first. Even learning how to do simple things like refining metal there is going to be hard. (See above, under 'engineering'.)
The idea is that if we plan to put humans at X, we start sending cargo drops to X every few months via the slow but cheap ITN.
After those start arriving at X, we send the humans. The ship for transporting humans only has to carry enough supplies to keep the humans alive during the trip. It doesn't have to carry supplies to keep them alive at X, or equipment to set up their base or colony at X, because those have already been sent via the ITN. The ship for the humans can be optimized for one task: moving humans fast.
Setting all of the above up working with materials from the Moon and from bases on the Moon will be a lot less expensive than doing it from Earth. First, the gravity difference makes it a lot cheaper to get something from the Moon to an arbitrary point (like one of those Lagrange points) than it does to get it from Earth to there.
Second, because the Moon has no significant atmosphere you can do things on the surface that would not work well on Earth. For instance, on the Moon you could build a long linear electric motor on the surface and use it to speed a vehicle up to escape velocity. Try that on the surface of the Earth and your vehicle is going to get destroyed by friction in the atmosphere.
The Moon is the key to long term human utilization of the rest of the solar system.
[1] https://en.wikipedia.org/wiki/Interplanetary_Transport_Netwo...
The Earth is very small, and the universe is very large. Eventually, we're going to want to use more than an earth-sized corner of it. Why not start now?
Also has it actually been confirmed that He-3 can be found in abundance on the Moon? I think it's assumed with good reason, but not necessarily confirmed.
There's your incentive.
There will be grubby, workaday incentives galore, all the usual politics, power, and pecuniae. "Because it's there" just grabs my fancy somewhat tighter.
"What is the real meaning of seeing this picture? I've always said, I've said for a long time, I still believe it, it's going to be -- well it's almost fifty now, but fifty or a hundred years in the history of mankind before we look back and really understand the meaning of Apollo. Really understand what humankind had done when we left, when we truly left this planet, we're able to call another body in this universe our home. We did it way too early considering what we're doing now in space. It's almost as if JFK reached out into the twenty-first century where we are today, grabbed hold of a decade of time, slipped it neatly into the (nineteen) sixties and seventies (and) called it Apollo."
Gene Cernan had poetry in his soul.
However if the costs can be cut by a couple of orders of magnitude, that picture changes considerably. All of a sudden the scientific payback in terms of geological insight into the history of the Earth/Moon system or resource extraction such as water and fuel become a lot more attractive. With SpaceX and Blue Origin working hard to do exactly that, it's quite possible we might return to the moon in a decade or two.