"We're not planting our flag and leaving. We’re going to stay, learn, and then go to Mars. There’s critical real estate on the Moon. We want to claim that real estate for ourselves and our partners, which is going to be critical to being successful in that mission."
Sean Duffy interviewed this morning on NASA+.
The Outer Space Treaty, which 117 countries, including the US, are signatories to, prohibits Earth nations from claiming lunar territory. The trouble with saying you can break any international law you want, by say, invading Greenland, or claiming the Moon, is that then anyone else can. By say, invading Taiwan, or claiming the Moon, also.
What do you do then, especially when they (China) get all the good bits of the lunar South pole first? Chinese plans for their International Lunar Research Station are far more advanced than anything NASA has. There's every likelihood they'll be the ones able to claim best the lunar real estate first.
Kelly and Zach Weinersmith (of SMBC, Soonish and other fame) wrote about this topic in their recent book A City On Mars (and have we really thought this through?). There’s a non-zero chance that there will hot wars on earth over utterly useless land and resources in space that we either have no chance of using or no need to monopolize.