"if governments disappeared tomorrow, what would prevent people from organizing again the next day, and compelling people to conform to whatever rules they devise in their region?"
Who would form the new government? How would they be selected? How would they enforce their will on those that resist (I'm assuming the military, police, lawyers, courts, prison guards, etc. all disappeared along with the government)? How would they raise money? Would there be one new United States, or would some states refuse to participate in a newly reconstituted union run by a bunch of complete unknowns? Would Northern California and Southern California finally get that long-needed divorce (it's a long way from San Diego to Sacramento!)? What if people took advantage of the chaos to introduce some drastic changes to long-accepted laws and customs, and what about people who object to those changes?
In short, if Mrs. Kravitz declares herself queen after the government disappears, commands me to take down my Don't Tread on Me flag and I tell her to take a hike, what then? How is she going to raise, pay, train, and equip an army/police force to make me? Creating a new government from scratch to rule a country is a very very difficult task, fraught with more problems and difficulties than any of us could possibly imagine. That's why most revolutions that topple governments tend to be very unstable (the United States being the only revolution I can think of that resulted in a very stable successor government(s), due mostly to the nature of the revolution - the top layer of government was simply exorcised, and everything else left as was)
I think a better book to read that directly deals with your question is Stephen King's The Stand, which is largely about the breakdown of modern civilization/government and its re-creation(s) in the wake of a catastrophic plague. The villain is able to create a new government and restore order quickly because, well, he's evil and has all kinds of Dark Powers. The good guys create a new form of government slowly, brick by brick and face many setbacks - and at the end of the book their society is still far closer to what you'd call anarchy than anything else.
For most of human history, people have lived without governments in tribal social structures that were essentially anarchistic. It is only in the last 10,000 years or so that the first governments apparently formed. I think the driving force behind the creation of governments is the division of labor - when you become dependent upon people you don't know very well to survive, a third party becomes necessary to arbitrate disputes. I think as long as civilization has a division of labor, governments in some shape or form will exist - but their formation takes years or decades. Look at Somalia for a contemporary example.
(if anyone is wondering, while I have strong anarchist sympathies, I would call myself a radical decentralist)