In order for Anarchy to work, the entire world would have to be Anarchists. Let's say if the United States was an Anarchy, other world powers would think of it as free land. After all, we wouldn't have a military. At least not an organized or an effective one. If the entire world was an Anarchy, then I will proceed to my next argument, Crime and theft would increase, and drug use would skyrocket, which leaves a drug abuser to violence, considering he has unlimited stock of drugs, and guns. Our communities would no longer be safe without police (which is government funded). Since their would be no substancial government, there would be nobody to keep any one in line. People would't do their job. If you're not getting payed, then why should you keep a job? Their would be no bankers, because there is no money to bank, which would make the economy plummet farther, and then there wouldnt be jobs at all. How would we obtain food without money, and people/jobs to sell it?
Anarchy also doesn't work because, say America was a country of Anarchy. Okay everything is all hunkey-dorey; no laws or anything BUT let's say China invades. We wouldn't have any organized defense. Or say England wanted control or else they would nuke us, who would make the decision? Obviously not s Government with no power over unruly people.
So now you have almost nonapparent Government, No police, no laws, armed and unsable citizens, no work, miniscule militia/military and no structure. Anybody could just do anything they want, and eventually you have mob rule. Warlords/Druglords/local terrorists or an armed, smart, and extremely dangerous rebel will just assume power. And then it becomes a dictatorship, which as far as I know, very few people like.