You should look further than the USA for examples. "Power vacuums" attract people who want power. When a warlard gets killed in an area with no effective government, another one steps in.
Democracy very quickly makes plain the scope of this challenge, and it's why it works with so much less effort on small scales.
Times are quite a bit different now; republicans control only the house, although the Tea party has radicalized them. I still don't know what that has to do with anarchy, though.
The mere idea of anarchy is itself inherently sensationalist - it's something that wouldn't happen without an apocalypse. It's also something that we can never evaluate "Scientifically" - we're not going to just disband a government and see what happens in the aftermath.
I think it's sensationalist gun-jumping, and does not take into consideration the actual economics at play (at least in the U.S.). Nor does it take us hackers as a serious economic force into consideration.
1. The Urban Archipelago: http://www.thestranger.com/seattle/Content?oid=19813
Nor does it take into consideration that the political compass is vastly more complicated than is popularized in the mainstream political theatre.
2. http://www.la-articles.org.uk/pc.htm
I don't have anything constructive to respond with in terms of "where women would fit in" given than your claim amounts to a biased post-apocalyptic scenario to begin with. (Also unscientific.)
Your abstractions I do not think are doing the work you want them to. The U.S. isn't some "macro-government" that can be thrown into the pot of all other "macro-governments." It's the U.S., and it's considerably unprecedented.