Email is a wonderful thing for people whose role in life is to be on top of things. But not for me; my role is to be on the bottom of things. What I do takes long hours of studying and uninterruptible concentration. I try to learn certain areas of computer science exhaustively; then I try to digest that knowledge into a form that is accessible to people who don't have time for such study.
As it turns out, even email is insufficiently immediate for many people these days. And nobody can reasonably dispute that when you're out and about, coordinating real-world social activity, it's sometimes better to have instant messaging — "[I'm] down the street, be there in a minute, stay put" is not a useful message to receive a couple of minutes late, nor do email's strengths offer much benefit in this context.
But you choose your communications medium based, to some extent, on the type of person that you want to be. If you want to be like Krugman or Knuth, then you need long periods of uninterrupted concentration, and you must favor asynchronous communication. If you want to be like a teenager gossiping about his/her classmates, then instant messaging is probably good enough. So, the question: do you want to be more like Don Knuth or more like... well, millions of people whom you've never heard of because they never accomplished anything great? Most of us settle for something in between, of course, but this is a question of aspirations, and anyway in practice the true issue is about modifying one's behavior at the margin and not about absolute positioning.
On the other hand, it is possible to take enforced inaccessibility too far. It is worth quoting a bit from Richard Hamming's classic essay:
I noticed the following facts about people who work with the door open or the door closed. I notice that if you have the door to your office closed, you get more work done today and tomorrow, and you are more productive than most. But 10 years later somehow you don't know quite know what problems are worth working on; all the hard work you do is sort of tangential in importance. He who works with the door open gets all kinds of interruptions, but he also occasionally gets clues as to what the world is and what might be important. Now I cannot prove the cause and effect sequence because you might say, ``The closed door is symbolic of a closed mind.'' I don't know. But I can say there is a pretty good correlation between those who work with the doors open and those who ultimately do important things, although people who work with doors closed often work harder. Somehow they seem to work on slightly the wrong thing - not much, but enough that they miss fame.