The reason you can make a claim in North America and have it stick is due to the U.S. Marine Corps and the U.S. Army. They are the guys that make it possible to make a mining claim and not have to worry about having some 2-bit thug come along and take your mine from you. That is what makes civilization possible. As much as Canada wants to assert their independence, they are dependent upon the U.S. military to make sure Russia doesn't go and sack the northern part of their country (or the whole country for that matter). Ditto for Mexico (in spite of the gangs in northern Mexico.... proving my point and the GP poster above).
The problem with the assumptions about those hoping for peace and tranquility in space is that you don't have sovereignty claims, thus no military of any kind except for pirates and thugs who don't give a damn about treaties or the United Nations. This also includes opportunistic nations that may want to take any space-based assets. That is not an environment you want to be investing billions or perhaps even trillions of dollars worth of money to develop space-based mineral assets.
Yes, space is big, far bigger than you can imagine. None the less, once you start sinking resources into developing a location in space, it becomes a target for aggression. That becomes a fixed point that can be occupied and stolen. Thugs will beat you up simply to steal ten bucks out of your wallet.... what will they do for assets worth billions? That is why you need to have available some friends who are far bigger and badder than any potential thug to allow civilized behavior to flourish.