I love the idea. Not so sure about the exact implementation details, but I think this is on the right track!

I wonder who would have to make the first move for this to become widely implemented. Facebook? Gmail? If Gmail and Google Plus teamed up they could jumpstart it.

As a rule service providers are looking to maximize the number of times they get in your face with a plausible excuse, not to minimize it. Gmail would like this idea, but Facebook would not. Hence, I don't see it getting adopted.

You can do this with Microsoft Exchange already, but not standard SMTP etc.

I like the idea. Also, I have the same problem with iOS notifications. If I've already read the update within the app, the notification should be cleared across all my devices where I have that app installed.