Though it didn't run iOS (and the little detail that it never came out) the "single computing device" model was one of my favorite selling points of the Ubuntu Edge [1]:
"From mobile... to desktop. Yes, it’s the full Ubuntu desktop OS used by millions on a daily basis -- and it runs directly from the phone, so you’ll be able to move seamlessly from one environment to the other with no file syncing or transfers required. The core OS and applications are fully integrated with their smartphone equivalents, so you can even make and receive calls from the desktop while you work."
"From mobile... to desktop. Yes, it’s the full Ubuntu desktop OS used by millions on a daily basis -- and it runs directly from the phone, so you’ll be able to move seamlessly from one environment to the other with no file syncing or transfers required. The core OS and applications are fully integrated with their smartphone equivalents, so you can even make and receive calls from the desktop while you work."
[1] https://www.indiegogo.com/projects/ubuntu-edge#/