A replacement for email should be a lot smarter and I think what pg hints at is pretty much the same as you're saying here, but broader.
If I receive an invitation to something, it should end up in my calendar and whatever gadget I have on me should notify me and ask me if i wanted to participate.
If i receive a receipt it should be stored and analysed. For example if the item had a 30 day guarantee it should ask me before that if I am satisfied with it.
If i receive a shipment notice it should automatically tell me on the day it arrives and alert me when I'm in proximity of the post office that I need to pick it up.
Actually I would want almost all of my emails to be read solely by a computer so that all of these emails I didn't even see. I don't need to see that I've bought something — I know that! I need to be told when its in my post box though, or if its a license key I need my computer to pop up a question if I should apply that license.
So a good startup idea here would be something that took your email, filtered it and just removed all of the receipts/etc messages from your view, while keeping it neatly organized somewhere else for the future.