Why do people hate email so much? (Because they haven't mastered it yet, Grasshopper, but anyway...) The thing is, it's communication. Are we shocked that a big chunk of our work burden is the burden of communication? "He spent 1/3 of his time at work answering emails!" Outrageous! vs. "He spent 1/3 of his time at work communicating with the other workers." Yeah sounds about right, if not a little low. The other thin…
He isn’t arguing against the use of email, but the non intentional default to emailing instead of work. Yes, your ideal scenario- communication between employees will get work done. But in Cal’s scenarios, that one person is having multiple conversations like that through email, and is waiting for the other person to reply. And instead of producing deliverables, they are having these slow conversations.
You mention just get to the email later, but rarely does the application or notification go away after the info is gathered. So your plan of checking email 1-3 times a day is right inline with Cal’s thinking.
Some of his solutions he hand waives away complexities with “we’ll rock and roll” but the idea is email won’t be a springboard for work. It sends pdf’s and reports and minutes great, but planning a project is better done elsewhere.