Given the following scenario: I want to contact someone completely strange. I don't know him or her yet (I'll stay with him for the rest of this article) and he doesn't know me. But I do have some e-mail address. I write an e-mail. And then I start waiting. Below, you find what's on my mind while waiting.
The point is that twitter eliminates some nasty things which come with e-mail. Twitter messages do not tend to disappear as they never leave the platform. I don't have to expect my message to be lost, e.g. due to spam filtering. The limitation to 140 characters makes answering a short twitter notice a task done without notably spending time (e.g. if my question is just whether my mail has arrived and will be answered... somewhen between tomorrow 0900 and dawn of doomsday). And even if I don't get an answer -- I do have an explaination. I don't get an answer because he does not want to send me an answer -- period.
WhatsApp recently (as in some months ago) added a feature indicating whether a message has been read by its receiver. Some people didn't like it for privacy reasons (and they have good arguments). But it totally fits the need sketched in the flow chart above: Most of us do like to know what happened after we pushed the "send" button and are more than willing to pay for it with revealing significant parts of our privacy.
Funny thing, once a communication with someone is negotiated, I don't care about mails needing days or weeks any longer. It's just like downgrading a network connection from TCP to UDP -- after the three-way-handshake passed.
Yet another personal note. There is a twitter account named "ad001" existing since 2k8. It's not mine.