And I think you are confusing anarchy with chaos.
And I think you are manipulating the concept of the "state of nature". To start with, you quoted Hobbes and Locke, yet I don't know why, you avoided Rousseau. I'm not saying you are being Evil Manipulator, but may I remind you your concept of state of nature is not precise. State of nature is a hypothetical state before social organization, it is the state of man seen as a non-social creature, something that is not defended by everyone. For example, I agree with Aristotle, unlike Hobbes o Rousseau, I believe man is social, thus this hypothetical state is not possible...unless in the hypothesis man is antisocial/asocial (Hobbes believes in anti-social, Rousseau in asocial).
Another mistake you make is to assume in natural state a man could freely trespass property. In fact, property is directly incompatible with state of nature. I should say more: In "Speech on the fiundamentation and origin of inequality between men" (found on other less pedantic titles), by Rousseau, he said private property was the responsable for the end of such state.
And about USA being the land of the free, I differ. And my arguments are found...
Here, and...here, and...here, and...here. Here too.
So yeah, there you have a bunch of reasons why USA is not a free country. No, I am not going to explain my opinion and arguments because it would take too long, and it would be a long pedantic post people would get bored of reading. But you can get only one of those if you are interested, you will see where things are failing, and it goes far deeper than any internet post.