Sending payments to fake addresses provides a way to broadcast short encoded and optionally encrypted unalterable messages to the world anonymously. Have security codes for the organization committing genocide, but scared you'll be killed if the publisher accidentally reveals your identity?

Publish them with Bitcoin.

Why would the addresses need to be fake? It is a good way to inexpensively referrence a purchase online. Say, for example, that you wish to order something from an automated commerce website that costs 205.53 bitcoins. There is still six digits of the bitcoin that can be used to imprint an order number. Say the order number is 633729, the total cost of the order would look like 205.53633729 bitcoin on the blockchain. Granted, the commerce site could issue a new address for every order, but what if they had some reason not to do that. What if each unique customer had an address assigned to them, but the ecommerce site desired to positively identify each of that person's orders from one another without requiring some kind of additional message parameters that bitcoin does not support, and even if it did, would provide TMI about the transaction.