Anarchy servers in Minecraft are very much unique in the way they let you play the game compared to other servers. While other servers might have rules against griefing, free pvping and destroying people's building, on anarchy you're free to do anything you could in game without cheating or hacking. This sort of freedom comes with some downsides as you might have caught on already. If you build the nicest building on the server, a good chance is it's not going to be there tomorrow. Surely someone is going to think the server would look better without it and make it happen. However these servers usually also foster the closest knit community since people are forced to make bonds of either friendship or rivalry with other players or they just keep annoying each other until one of them moves on.
While you may think that Minecraft anarchy servers are some of the more sparsely populated you'd be very wrong about that. There are plenty of people more than willing to take up the challenge of playing in the wild west, a dog eat dog world if you will. Most also do it for the bragging rights, since few can say that they have a standing building of their own on an anarchy server. This added thrill makes the game quite a bit more fun since it drops all the dead weight of rules, while letting you quite literally wage war on your fellow players if you so choose.