Given the exponential power growth of smartphones I am sure this will be possible by the end of the decade. Actually we already have 2.5ghz octacore smartphones now, so probably already possible.
That being said, what stops you from running a server on your phone today?
I've been using my phone as a backup git remote for a few years: https://play.google.com/store/apps/details?id=net.antoniy.gi...
I already have a small phone farm like that for testing stuff, just not actual hosting.
Never tried to build a whole linux hosting environment on a phone though, not enough motivation because they haven't been powerful enough yet.
Could be a super cool mesh network thingy, (wasn't Diaspora supposed to do this?) bitcoin?
Mobile phones (and their networks) are under heavy surveillance.