>Rule #1 of Kanban is that it is a "pull" system. By design e-mail is push. It would also be difficult to limit work-in-progress here, which is another cornerstone feature of a Kanban system.
I was actually just thinking about this the other day. To rephrase it slightly, an email inbox is essentially an opt-out model. Any person anywhere can put something in your inbox, and after reviewing/getting sufficiently annoyed you can opt-out from receiving their emails (marking them as spam, forwarding to trash, etc.)
Personally I've been interested in seeing how an opt-in inbox model would perform. Every email goes to spam and/or a review bucket, and then once a week (or whenever you feel like it) the user can skim the bucket for emails from people/lists they actually want to see, and approve them. Follow up emails from those address can then go straight to the inbox with out need for review.
This might not work for every use case, but I suspect I'd like this for my personal email use. No matter how many times I unsubscribe from an email list or service, a new one takes its place without me signing up for it. I think I would find significant less frustration being able to opt-in vs opt-out.