Well, the baby of Facebook and Basecamp would definitely be online, which makes it impossible for it to even want to compete with email.
If you cannot search, read and write messages OFFLINE it has failed in my eyes. Outside of silicon valley or whereever, there are places where you will not get a connection.
Furthermore, it'd have to be more of a protocol rather than a service itself. many companies will not rely on some third party for hosting their most valuable information and communication network. same goes for individuals, probably <1%, but that is the tech-savy crowd...