I can see where he's coming from, as a large number of my daily e-mails are things that I'll never read or have only minimal need for (HR's health reminders, vendor spam, several conversations where people hit 'reply to all', several more conversations where someone doesn't know who to ask and so asks everyone, etc...). At the same time, however, your points are all valid. Technical requests really should be in writing for reasons of both CYA and for specificity. On the gripping hand, our engineering staff only ever uses e-mail to disseminate notes and how-tos. The primary means of communication there, especially when troubleshooting problems, is IM (Lync, unfortunately). Both have a time and place, and the trick is knowing when to use each.
Having said that, e-mail is probably the one piece of tech that I'd love to kill off entirely if I could; even sooner than I'd kill Flash or Java.