@novalysis
After a further explanation I think I understand now that you are not using society to refer to the human society in which Madoka takes place, but rather the the society of Magical Girls separate and apart from the rest of human society.
Well duh. Of course it's an anarchy. Not only is it a society with no adults, but each individual member has enormous combat power and an extreme incentive (survival) to compete for scare resources. Additionally, the members of this society have a very short life cycle. The evidence seems to be the both Kyouko and Mami were rare magical girls for surviving so long. Kyouko is estimated to have been a magical girl for a couple years. Mami perhaps a year longer. (This fits with being contracted in middle school and Mami being in high school).
It's an inherently unstable society. A libertarian Magical Girl would not be any more interesting then any other girl who thinks a lot about government or politics. I don't see how libertarian ideas would help in any way (and I say this as a libertarian myself).
More interesting might be to take a character like Mami and give her some kind of motivation to institute order in the Magical Girl society. That is in fact peripherally explored in this fan fiction:
To The Stars
Mami is the natural pick because she has the following advantages:
1: Mami has a slower rate of "mana" consumption compared to other magical girls (as Kyubee revealed to Sayaka in episode... 5 or 6 I think it was). This would allow her to spend more time and energy on forming a more complex society.
2: Mami enjoys society, she is not a loner by nature.
3: Mami is a motherly mentor figure and likely to be persuasive at getting new magical girls to join.
It's actually not surprising that any Magical Girl team we see form tends to be around Mami.
However, Mami lacks the ruthlessness needed to force others to obey her. Nor does she recognize the need for "farming" familiars to produce more grief seeds, and you would need an excess supply of food before building a society.
Kyouko might have some of the needed ruthlessness, and so she might be another pick to build such a conceptual Magical Girl society around. However, Kyouko is a natural loner, and lacks the persuasive ability or vision.
So either you'd need a character who blends Mami and Kyouko's traits together, or you'd need something like a team up between Mami and Kyouko.
That might be an interesting AU. Mami and Kyouko at their first meeting. They team up and instead of breaking apart over ideals, Mami compromises her principles to "farm" familiars. Mami would be in charge of things like recruitment, training, and peacemaking. Kyouko would be in charge of enforcement, and distribution of grief seeds.
Essentially recreating a family unit with Mami as the mother and Kyouko as the father, and other girls as adopted daughters. Assuming they were able to determine the truth about Soul Gems and Grief Seeds they could then start planning a way to manage their resources.
This team would need to expand it's territory to increase the number of grief seeds being brought in. By working in a team of hunters they could expend less magic during battles. The main difficulty would be that since less Magical Girls are becoming witches they would need to lean heavily on farming familiars. That means they would probably have to determine how and when witches spawn familiars, how to encourage spawning even, and to hold off on harvesting the witches until the familiars are spawned.
This would increase the bad things happening to humans. Something that I think Mami would have a very hard time with.