The world is not a graffiti free-for-all because there are barriers: the government (police) is able to apprehend individuals, link that physical individual to an identity (which it issued at birth), and effectively implement consequences to that identity/individual.
If you want your site to not be a graffiti free-for-all, you will need a durable way to identify actual people. Twitter, for example, essentially requires a phone number to use their site. Phone numbers are fairly difficult to get anonymously. Therefore, Twitter has a useful link between their users and a physical individual. Other services use other things.
The government should implement cryptographic certificate based identities to citizens. Ideally there would be a way to "sign" something that says you are a real citizen without revealing which citizen you are, but is durably unique (subsequent signings identify you as the same citizen).
Facebook, Google, etc. are effectively filling this function right now but they leave much to be desired.