I think this is a brilliant idea, and someone will eventually do it.

Richard Branson already organises meetings where you donate a few thousands to a charity of his liking in order to have access to a dinner and a chat with him. Why wouldn't he add a few dollars to charity per email AND mitigate his inbox problem a at he same time.

Also I love the idea of an automated system to adjust the asking price as f(total unread messages)