Can you keep typing on this train of thought for a bit? I was interested and didn't get enough here.
You know how sometimes you have a thought and don't realise how much of it's working on unexpressed assumptions within your own head? Let me have another go.
It starts from the assumption that without structure it's a pure might-makes-right free for all; everyone is an individual and is entitled to what they can hold through force. Basically extreme anarchy. I don't think that such a system is stable for long, humans are too risk-averse to put up with the idea that they're constantly one unlucky bullet/spear/knife away from losing it all. And so they'll try and optimise their relationships such that that's not the case.
The other option is cooperation with at least some number of other humans. This is assumed to give generally better outcomes overall than might makes right. And in a lot of basic situations it can be gamed out as a kind of prisoners dilemma. I have excess oranges that you want, you have excess apples that I want. Either of us could attack the other, and perhaps get what we want at limited personal cost. If we both attack each other, we probably both get injuries and damage. However we could just trade, and both get what we want at no risk and no real cost.
That this works in just about any single simple scenario means that people will then look to continue these sorts of engagements, because agreeing to also cooperate in the future works to everyone's benefit. And they'll look to generalise to other similar areas to form things like trade and monetary systems, because that's useful.
This is now becoming structure; people have taken a one-off scenario where better outcomes result for all parties and started to behave in such a way that certain behaviours are expected in the future. There are reasonable expectations that other people will behave in ways other than "he'll shoot me if he wants my stuff", and as lots of individual expectations combine there arises the complexity that constitutes a society. This is now a large group of people with established conventional modes of behaviour that are mostly not violence.
As far as the government stuff, it seems natural to me that as a society grows in complexity it gives generally better outcomes to have people specialise to a certain degree. As a kitchen in a restaurant grows bigger, it becomes beneficial to have a butcher chef, a pastry chef, a saucier, a kitchenhand, a dish pig, and so on. Similarly, a society ends up with a guy whose job it is to mediate disagreements, or to manage resources, or to plan development.
These sort of middle management roles could be considered a sort of government; they're ultimately responsible for things that affect all or a large portion of the society. Depending on the structures that put them in place, they may be little dictators doing whatever they want, or they may be unable to act unless their proposals meet with majority or even universal acceptance. These are the differences in all the political systems that we see; how are the actions of people who may affect large segments of the population restricted or controlled?
But I don't think that there's any particular roles that are "required" here, a society could choose not to have a certain specialist. An internal military like a police or a sheriff is a specialist; they use force where not doing so would cause greater harm to the wider community. A society could choose to have it's citizens be personally responsible for the use of force (something I think the US tends to lean towards at least in principle), and such a specialist role would then be largely redundant.
Would you say then that human cooperation (more generally) is needed to protect rights?
Yes.
That's what rights are, logical statements that lead to stable systems of entities interacting with each other because everyone chooses to recognise them. If you're not cooperating and just doing whatever you feel like, then rights don't come into it. That's might makes right.
Just like numbers and basic arithmetic are something that people can objectively agree on to form math, the axioms of rights are something that people can objectively agree on to form stable and useful systems of interaction.
This doesn't mean that people
have to agree, I can assert till I'm blue in the face that 2+2 makes 117, or 43, or both 117
and 43, and that just makes it impossible for you to have a mathematical conversation with me. But if we do choose to agree, then we can work together in ways that would not have been possible while I was being a mathematical imbecile.