It's a free country and you are free to measure productivity however you want. That said, is this slow societal descent into short, insincere, 140 character coke-addict emails with expected instant response times a positive thing? I'm not trying to be nostalgic for the letter-writing days of yonder, but nothing says "I don't give a shit" like those emails you get. You know the ones. 18 people are CCd. People just attach whatever they think is relevant without reading what you're asking. People forward whatever to whomever. This guy to BCC. So and so will arrange. Have a look at my calendar and suggest a time. I attached version 2 Final Revised Signed Real Version Final Final. Blah blah blah.
People were productive long before death by instant email papercuts. It's something worth thinking about as you optimize on response time. I find many insta-responses were preventable with better planning in hindsight.