As I see it, the real power of email comes from the inherent queuing nature - it allows you to decouple your schedule from demands of others.
Being "realtime", especially if the senders have the expectation that the message is realtime, means necessarily losing that queuing nature which greatly diminishes email's flexibility and resilience.
The biggest problem with realtime is that you _need_ to implement some sort of access control, or otherwise you'll be inundated and overwhelmed with messages. If we turn email to realtime, we'll necessarily need to build the access control (or some sort of super filter) into it, and that basically shuts down the open nature of email. You can argue that open email is good (emailing Steve Jobs) or bad (spams) but it _is_ something that has real value.