This works great for small-scale things, such traffic laws or even small communities. On a large scale though, foreign policy, military, social programs, etc. would go to hell in a handbasket. Unpopular service jobs that we take for granted, like trash collecting, without pay incentives, would collapse. This would leave each individual with many more responsibilities and would ultimately detract from everyone's quality of life
In the end even if a large society managed to act civilly with one another and the core principle of Anarchism was achieved, the weakened infrastructure and military of that 'country' would make them a target for every other country who wants to expand their borders.