Some contradicting quotes from Mr. Karp:
“I used to suck at e-mail. I'd let e-mails pile up, get overwhelmed, and miss important messages, or forget to reply. So I set up filters on my e-mail, and that's been working pretty well. Now, my inbox gets e-mails only from people in my company and from my girlfriend. A folder called Robots gets anything not written by a human, like bank statements and Google Alerts. Most everything else goes into the Unsorted folder.”
“We mostly use e-mail to communicate. I love e-mail, because it doesn't interrupt anyone. The fewer distractions, the better.”
This goes against two of your points:
If something is really important, you should talk in person AND don’t email someone you can literally see from your desk.
Tumblr is fun, not something to replace email – no one really uses personal message factor on Tumblr. In my 6 or so years on Tumblr, I’ve never received a personal message.