I always assumed that if all government was removed and it was just a free-for-all, it wouldn't take very long for groups of people to start banding together to protect themselves and their property.
Because you would, right? You'd talk to your neighbours and sort out what was going to happen if someone burgled one of your houses, and maybe you'd set up a little pool of money for improvements to parts of the local neighbourhood that didn't particularly belong to anyone, and generally just get stuff done that would make life easier for everyone.
Hey presto, you've got government again, albeit on a tiny scale. And it grows from there.
Government is a side effect of it being helpful for people to co-operate with each other. Unfortunately, it sometimes grows out of control or is enforced with violence, but in almost any group of people of a reasonable size you'll see this sort of thing turning up.