Because you can send messages to steem users, without needing to trust any party. Plus, you are guaranteed that your recipient only can read your message. And you are sure that your recipient is who he claim he is.
For example in steem.chat and discord, many people were scammed because of some guys creating accounts with the same name as some whales here. With SteemMessenger, you are 100% certain that if a person messaged you, it is real. If you make an app for messaging without this steem memo key, anybody can start scamming other people by using someone else's name.
A centralized server isn't necessarily a bad thing if used correctly. If messages were stored in the blockchain, imagine in a few years, with the rise of quantum computing, it woud be unsecure to have all your private messages in a blockchain, ready to be "brute forced" by anyone. And even if Steem evolves to become "quantum proof", all your previous messages would still be encoded with a deprecated solution. In a centralized server, you avoid those issues, because people can actually delete their messages as they like.
Solid answer. That actually makes a lot of sense to fight phishing and I can see it becoming a very useful tool once it is perfected thanks to it's open source nature guaranteeing that your server never even sees the private keys.
Thank you for your in depth response and good luck on the project!