I've argued this one a LOT on the internet, (I have no life, really

) as the idea of "claiming" land here on Earth "works" because it's enforceable. When it can't be or isn't its ignored.
Hence the Nazi "claiming" a majority of Antarctica was never taken seriously by anyone else. (Or certain claims of "colonization" by some South American countries today for example)
However the entire "basis" of the argument is the "fact" here on Earth that land has an inherent "value" over and above any possible resources that it has. On Earth you have pretty much "free" basic life support even if you do not have any "resource" rights so therefore "land" has value and can be used as a commodity. (And as a "basis" of that process a "government/nation-state" has to OWN the land before it can be "granted" to someone else hence the need for governments to "claim" territory which is the basis of all "property' on Earth)
This is NOT true in space. Owning several acres of the Moon "land" wouldn't be the same as owning the RESOURCES of those acres. Once you've harvested the resources the "land" is useless to you. You can't "live" on it without a lot of intensive resources and infrastructure IN-PLACE already so the American "frontier" mindset of "ownership" is pretty useless. It's just not the same as on Earth.
Randy