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To summarize, the libertarian solution is the self-betterment of the individual.
That's half correct. Libertarianism claims that its scheme will, on average, lead to the self-betterment of the individual, but it do not tries to force that on each individual, rather, it leaves to each individual to either enjoy or suffer the consequences of their actions, which on average will lead to most men to get better, not all. Libertarianism is "liquidationist" both in economical and social terms.
I am not optimistic that the common man will learn to "understand and cherish open, rational discourse" and "take an active role in continually improving their own beliefs and evaluative principles."
Libertarianism tells you that you don't have to be. Be mindful that any other option implies to trust decisions to centralized authority. Even in democracy that implies that you are trusting the decisions of the many in a few, so those who are not trusted to take their own decisions are trusted to decide who will take all decisions for them. It's an oxymoron. Libertarianism ends all of that nonsense and leaves every men to pay the price of either their wit or their folly. Even if that implies most men will fail to their folly, it will still be better than any other scheme which can only lead to all men to fall in such circumstance.
It's not a matter of absolutes, it's a matter of averages, robustness and overall outcome.