The author includes the following quote, with which he apparently agrees:
“If email was invented today, it probably would not have survived as a technology,” Mr. Suarez said. “Social and public sites are much more efficient.”
That doesn't seem remotely plausible to me. If a company wants to send a message to a customer, a supplier or its lawyer, they're not going to do it on Facebook (with its dubious privacy policies) or post it on Twitter (for everyone in the world to read). And a sender can't rely on a recipient even having a social media account on the platform they use. E-mail, like the telephone, is both more universal and more private.
Also, in industries like investing or software development, where communications need to be archived so that they're available for legal discovery (e.g., SEC enforcement actions, or establishing prior art for patent litigation), your company needs to have control over its own e-mail. Saying "We can't respond to your subpoena because Facebook deleted our trader's account for breach of its terms of service" won't make government regulators very happy.
Finally, you might be able to declare "e-mail bankruptcy" in your personal life, but if you work in the business world, you can't just throw away all your e-mails after you return from vacation (unless, maybe you're the CEO of a company). You co-workers and customers aren't going to appreciate your dropping the ball on important issues. One solution would be to set up e-mail filters so that e-mails can be categorized by priority and the urgent ones replied to. For example, if you're a blogger for the NY Times, comments from your readers shouldn't even be going to the same e-mail address as messages from editors or news sources.