It doesn’t matter if you want a government or not. People will still find a way to become powerful. It goes back to our most primal instincts of having tribes and packs led by alpha males. We are social because of this instinct to be led by one powerful person.
In anarchy, there wouldn’t be one leader. There’d be many. These would at first be simple gang leaders. And something tells me they won’t be as nice as your run-of-the-mill legislator. Let’s just say that, if you want to be powerful quickly, assault rifles are your best bet. In a few years, you’d have several powerful despots and dictators, loosely bound by their country of origin.
If you want an example, check out Haiti right now. The government’s pretty much collapsed and it’s every man for himself. It’s a complete fight for survival, complete with necessitated looting. Even the military, without complete leadership, has gone wacky, and have commenced riding around in pickup trucks and shooting AKs at people they think are breaking the law (AKA hunting for food in the rubble in order to survive).
Do you really want that? Do you really want a lawless nation where anyone can do anything? And where not-so-nice people will still come to power regardless of what you wanted in the first place?