I want to start this by making an important distinction in my mind between what you might call justification and rationalization. We justify arguments; we rationalize institutions. If you make an argument you have to demonstrate to someone that you have grounds for making that argument. If I were to say "human life would be chaotic and inconceivable without government" I would have to justify that statement. If I were to say "human life would be a peaceful spontaneous order without government" I would have to justify that statement too. But these are propositions. It doesn't make sense to justify institutions that have evolved and exist pervasively, like government (or markets or family for that matter). Do you consider families illegitimate unless you have some philosophical justification for them of the sort that Mattheus von Guttenberg demands? No, that's nonsense. Families just are the way we appear to organize ourselves, because "that's how it's always been done" (of course it's never actually how it's 'always' been done, but that's how it seems to us). So part of the disagreement here is simply that Mattheus seems engaged in a project which itself strikes me as a little silly (but which is invested with a lot of significance by some people).
Now, there are plenty of good reasons why we may not like institutions (like government). In this sense we would definitely hope to have some rationalization for the institutions that do exist that we find convincing, and insofar as those rationalizations fail we may even want to try and change those institutions. This makes sense to me. But these are of the form of "governments are good because they can provide public goods", or "governments are bad because they are coervice" which is really not the "justification" that Mattheus wants.
When I say that social contract theory is silly I mean that it seems obvious to me that government doesn't find its origin in some compact between the government and each citizen. That seems relatively trivial to toss out, and while it might have animated my views way back when I don't think I've thought anything like that in a while. In all likelihood neither you nor anyone you've ever met (maybe with the exception of naturalized citizens?) have ever explicitly contracted with the state. It's hard to argue that we tacitly contracted with it either, since our choices are relatively constrained. That's not the origin or nature of the relationship that people have with the state, so it's hard to see how such an arrangement could justify the state. The relationship people have with the state is that they were born into a society where the state was an important institution of governance (I think Joe Fetz's distinction between the state and government is important), and they went along with it (yes, my dear anarcho-capitalists - almost all of you have gone along with it every bit as much as I have).
But as I say in the title, variants of social contract theory still make great bedtime stories. What is a bedtime story good for? It reassures you and the good ones give you a simple explanation of a real world phenomenon that's still grounded enough to be meaningful. That, I think, explains the appeal of social contract theories to a lot of people. That also explains why people talk like social contract theorists even when they're not trying to engage in any formal justification of the state. We feel like there's something good about public service and being responsive through elections and putting our views out to try to steer our democracy. We feel like it's good to read and defend the Constitution. We feel like we owe something to the maintenance of this government, because generally speaking we feel like it's a pretty good institution. And we also feel like the government has an obligation to all of us, and that if it fails in that "it is our right, it is our duty to throw off such Government". We also think that all of us are more or less in this sort of position. So social contract talk is a good way to encapsulate all that.
But saying social contract theory talk is a good bedtime story is very different from saying (1.) the state emerged out of a social contract, or (2.) social contract theory justifies the state.
As I said above, it doesn't make sense to me to "justify" the state. The state just is (for now). You decide whether you like it enough to go along with it, or maybe if you like it enough to go along with it but work really hard to change it.
The state is coercive. On its own, that's probably a mark against it, until you realize that coercions pervade human life (indeed, all life). When you realize that, the goal subtly switches from rejecting coercion to minimizing coercion - and minimization of coercion may involve a state. Mattheus looks at the coercion of the state and says (I'd suspect) that it must be justified if it is to exist. I'm skeptical of this precisely because I see a lot more coercion out there. The violence of competing tribes of humans and the coercion implicit in the variety of externalized costs of transactions make me wonder about the implicit assumption that when we remove the coercion of the state we reduce coercion generally. Remember also that property itself is coercive. No one is born with property except maybe their own person. Property rights are constructed and coercively limit the actions of others. The state is coercive to a large extent because it protects and in many cases defines these property rights. Without the state, the establishment and exercise of property rights will still be coercive (and that's a good thing - property is a tremendously valuable and civilized social construction). But it makes this issue of making the state contingent on a justification hard for me to swallow.
So I don't usually "justify" the state. I do think a lot about elements of states that I think make states good or bad. These include democratic decision making, decentralization of power, explicit constitutions limiting state power, and a mission of providing for the welfare of the people. You can have various theoretical and empirical arguments for each of these (and you probably should have both).
Some of these explanations of course are very similar to enlightenment approaches to justifying government? We economists know that proofs of democracy as an arrangement for maximizing a social utility function is bogus. Indeed, we know that the very idea of a "social utility function" is bogus! But if we think that people have different preferences and demands, a good way to keep the actions of the government roughly in line with those preferences is probably to give everyone a say in the government decisions so that the average vote is amenable to the average citizen. So long as the citizenry has common needs and views, that should work OK. Insofar as it doesn't, you decentralize the locus of decision making until it seems like it will work OK. That preserves the contours of a "will of the people" highfalutin philosophy of democracy, but of course it isn't one - it's just a general assessment of why democracy works OK (and why democracy plus decentralization is better than just democracy). And it's certainly not an explanation of the origin of democracy (although it's probably safe to assume that other people thinking along these lines helped put democracies together). Fancy philosophies of democracy reinforce these rationalizations, which probably explains why we try to justify government with philosophical arguments. Attempts at justification in that sense may be functional. We probably benefit from convincing ourselves we need to justify government because these justifications can get us thinking along the right lines (I obviously don't contest the tone of social contract theory or enlightenment theories of government). But I'm skeptical of the extent to which justification is strictly necessary.
I think this is what most people do. We rationalize and judge government, but we really don't justify government. If you want a "justification" of government, I'm not sure I have one. I do have many opinions on it, though.