With the respect to the Nozick thing, I have similar criticisms. It is, of course, a thought experiment, which gives Nozick some license to set the rules. And the rule he sets, near as I can tell, is that people will behave in exactly the manner Nozick needs them to in order for him to make his theory work. They are generally virtuous in a state of nature and generally respect everyone else's rights (borrowing heavily from Locke on this point). They misbehave just enough for Nozick to justify the evolution of a minimalist state (through an immaculately rights-preserving process), and not one ounce more. It's all very convenient, very shoddy. None of his assumptions or suppositions about the way people will behave in his model are discussed or defended, it's just delivered as "this is what will happen". Well, if we're all willing to buy these 1001 assumptions and conditions, then yes, this is a fine theory. I'm not a fan. Apparently it's a pretty well-known book in the field though...
Moving on to the meat of the discussion: democratic process. Your main thrust is that culture is the significant element, rather than institutional structure. I have a hard time disagreeing with that, and the archives of this blog will show that I've made the exact same argument with respect to democratization numerous times. However, as you note in your final paragraph, there is a symbiotic relationship between culture and social institutions. Institutions are products of culture, but also vessels and conveyors of culture. Properly understood an institution includes not just the bells and whistles, but social understanding the underlies it. Institutions, as you note, express and establish norms. And given the general chaos of cultural "progress", institutions may serve as one of the best means of trying to place a twig in the river to redirect the flow (to the degree that it can be consciously directed at all, which I assume to be a fairly small degree). I'm not sure that institutional objectives and cultural objectives can be cleanly divided.
I think it's also important not to fetishize an ideal culture, as that may prove as illusory as a true state of nature. One of the most powerful insights of our founding fathers was that people are flawed and will always be so, and that institutions of government must be built to withstand imperfection. I'm not suggesting that those institutions could survive total cultural collapse, but rather that they can be built with certain tolerances, and even built to provide some self-correcting mechanisms that will feed back into civic culture.
Also, I have to take issue with slippery slope argument against non-minimal states. Frankly, the regulatory tide has generally been receding in the US for the past 25 years or more. There has been a strong push towards deregulation in many areas, particularly the traditional regulated industries (power, gas, telecom), as well as in some populist areas (welfare reform). The judiciary has been overrun by Chicago school libertarians and antitrust regulation has been rendered virtually non-existent. I don't see a slippery slope at all. We careened towards libertarian excess in the first couple decades of the 20th Century (known in legal circles as the Lochner era), then over-corrected through the middle part of the century, and I think are now trying to establish some sort of balance.
Finally, I think you should be careful in assuming that if there were an ideal culture it would be a libertarian one. I think a strong argument can be advanced that the best approach to social justice and social institutions would be something along the lines of Rawls's two principles of justice (although I don't think Rawls has made that argument). I find it to be a far better fit for our intuitions about justice than a libertarian institutional structure. According to a theory like Nozick's, if A is born with every possible advantage and goes on to great success, fame, wealth, and power while B is born with every possible disadvantage and ekes out a miserable existence before succumbing to a preventable disease, then A deserved everything he received and B was entitled to nothing more. This Nozick would call this justice. Rawls would cry injustice, and frankly I think so would most people. And I think that even if people took Confucius's advice and acquired knowledge and insight, they would probably still agree with Rawls. It seems quite plausible to me that even if we had a state of remarkably educated, diligent, civic-minded, and rational people, you might find that it is still a non-minimal state.