I believe Apple looks at the problem this way. Rather than have one piece of hardware act as all devices, they have multiple pieces of hardware that share the needed parts. (Though they haven't finished making it quite as useful as I'd like it to be.)
One of my concerns has been privacy. In this case what I mean is that I don't want Apple or Dropbox or Google or Canonical to own my data in it's cloud. I would probably be satisfied with a solution that only stored encrypted data in the cloud so that those data storage providers could not possibly access my data (so they couldn't be allowed to have my encryption key). I would also be satisfied with a way of hosting a cloud storage platform on my own servers (which would likely be a VPS, so I'd have to encrypt it anyway or else Linode etc. would have my data).
If we go the route of using the phone as the center, then we also need to add the capability into the Linux kernel to connect to external computing resources, like CPUs and GPUs. Then we're not limited to just a "thin client" type of desktop, but could have a full powered one.
Currently, i am carrying my laptop from and to my workplace and i'd like to get rid of that.
My guess is that the current highend phones already suffice for most of my work. The one part that is missing is virtualization for the occasional VMWare use..
No internet required.
I suppose the same thing is possible using local wifi synching, like how Dropbox shares content over a LAN when it can vs. downloading it from the cloud.
With the network this bad (cost and performance wise) in US (due to legal and monopolistic reasons, not necessarily technical), that makes a pretty shitty computer. So I would rather have a computer that can be divorced from the network if need be.
I also can't wait until the day we don't have to charge our mobile devices (solar + kinetic charging in every phone)