That's EXACTLY why we have governments. Humans can't self manage, we fall prey to our baser instincts too easily (Especially the "Me before you" aka self preservation aspect.).
We may have been able to pull it off long ago when people lived few and far between each other, but now that we live on top of one another, and our current living situations are VERY fragile, if the governments just poofed and no longer existed, then it would devolve into complete mayhem within a week.
Hell just look a city wide power outage in some major city. A single night without power, and there's almost guaranteed to be looting. or. Holiday sales. People will literally trample other people just to save a few bucks on some piece of electronics.