What Nick Bilton is really saying is not that email isn't good. But that the people that are sending him email aren't important enough to reply to. I'm sure he's not going to fail to reply to an email or (change the method of communications) with Arthur Sulzberger (Times publisher) or Larry Ellison.
I'm sure if he looses his job at the NY Times, and has to find a job, email (and the people that write to him) will take on a new importance.
While I don't get 100 important emails per day I do (as many people) get plenty of emails and I almost always respond to any that are personal (and not spam or sales pitches to which replies are optional) to the best of my ability as quickly as possible. I'm glad I get emails.
Nick (with all the out of work journalists) sounds a little like the celebrity who is tired of being hounded by paparazzi. Or the pretty girl who doesn't like all the attention from guys (see what Cybil Shepard has to say about that now.)
Email still has a place in communications and serious business and many other things as a communication medium. It's different if you are a teenager of course.