I continued working on this as a small side project and I really like the direction it's going even though it'll never be developed.
Some infos:
I'm still not really satisfied with the icons and will probably refine them later. The gestures and interactions aren't really specified yet.
The blurred background is based on the user's avatar. If there is no avatar, it'll change to a default one.
Feedback is much appreciated!
I also put this project on LayerVault and made it public. So make sure to check it out: https://layervault.com/pxlpk/iOS%20Mail%20App
(I did the UI in Sketch. :))