I think improving email lies before the client. Email is just a message container and apps generally throw a load of different content into that container, events, to-do's, photos etc.

Some of this stuff should never arrive in my inbox. A to-do email should automatically go to my to-do list, an event should automatically go to my calendar, photos should automatically go to iPhoto (or whatever).

Separately to that I can choose how I'm notified about that content.

For example, for all the marketing emails, I'd much prefer to have a Flipboard type app on my mac that receives all of those messages so that they never arrive in my inbox.

So no, email is not broken, but we haven't kept up with ways to manage the growing number of correspondence email is handling. I think the solution lies on the server where mail is sorted into types i.e. if you have that Flipboard for Marketing app, you get those marketing messages otherwise you don't.