"How is all land claimed given that the vast majority of it is untouched and unhomesteaded?"
Feel free to go to some of that unclaimed land and claim it. It will last until someone stronger comes along and takes it from you. That is the only true natural law: Survival of the fittest. Government provides a means to protect the weaker members of society from stronger ones. You claim there's "no evidence" of the services you received... well, that's because it's hard to provide evidence of something that didn't happen. For instance, Canada and Mexico didn't send a battalion of soldiers to your town, rape and pillage it, then levy a heavy tax on the rest of you. That didn't happen because the US Army protects our borders. (I'm assuming you live in the US, obviously.)
There's no real "evidence" that this protection worked, sure. That gives you a nice loophole to keep screaming "no one has provided evidence!" But that's an utterly ridiculous attitude. You can look at history and see what happens to regions with a weak military. They get conquered.
Now you get to cry argumentum ad baculum. Because, of course, we you can't craft a reasoned reply to a realistic point you can always fall back on screaming logical fallacy!