Minecraft is a pretty varied game when you think about. People find new ways to have fun in this game every day whether it be by competing with others or just hanging out with their friends, talking about their days. Minecraft anarchy servers are about as smack in the middle of those as can be, since while they're definitely not competitive, since they lack any concrete rules and ways to measure ones success apart from simply how long you have managed to survive on them, they are also not quite casual since that same lack of rules also pushes them from the territory of relaxed into a constant feeling of anxiety of having to proverbially look over your own shoulder so as to not get jumped by someone or a couple of someones looking to ruin your day, by blowing up your house or taking your precious mined treasures that you found after a long day of exploring.
However there is certainly a type of charm there that most of the other game types lack, such as the fact that you basically make up your own rules as you go along, there's not going to be a mod that's going to bail you out once you get attacked by others neither are they going to rollback the server if your stuff gets blown up by a couple of griefers. On the other hand though, they're also not going to interfere with you going after them, either by killing them and taking your stuff back or getting your revenge by mining through their base and taking what you please.
Sure most people are going to be turned off by the dog eat dog server type, however a few people are going to enjoy it immensely and a fewer still are going to thrive in such an environment. There are quite a few different servers offering this game mode out there and it's slowly becoming quite popular on the usual Minecraft server list. You're going to want to shop around a bit though since you want to make sure to be able to get along at least a bit with the people on the server, since your fun is going to depend on them as well.