Latency and bandwidth means we're far from a situation where this is viable. Even locally in my house, wifi speeds are a painful limiting factor for some things.
It's also increasingly irrelevant if I carry a powerful computer with me anywhere to have it instantly available anyway. The only thing stopping your phone from having terabytes of storage today is that it's currently expensive, and not much demand for it vs. the slight extra space it would take (512GB SD cards are a thing, but apart from size - though micro-SD versions are bound to follow soon - the cost makes them prohibitive for the next year or two).
We're very rapidly approaching the point where - while there may be value in having everything synced to the cloud for backup and universal accessibility - you'll be able to store all your data on media smaller than your thumbnail. Storage density appears to grow far faster than peoples storage needs at the moment.
Well just look at how quickly we fill up phones with lowest-tiered storage (although this is artificially contained). There is also a technical hurdle of building apps in a way that they can be "lazy loaded" — my phone's 4G is the fastest internet I have access to (in Melbourne, Aus) so it's not inconceivable that the "core" 10MB of Facebook.app would be ready in seconds, with the "full" 77MB installation ready in under a minute.
Personally, my phone is full of photos. Cloud syncing allows for recent photos to be on-device and instant, while there's more than could ever fit on my phone stored just seconds away. Once Photos.app and Facebook.app are on-device, I could sign in with my cloud credentials and they automatically log me in and all my content is "just there" (this is true today). When we can log into any device, display "my" home screen with not-locally-installed YikYak.app (46MB) and run it on-demand we'll see true portability of profiles and portability of devices will begin to take a back seat.
It's also increasingly irrelevant if I carry a powerful computer with me anywhere to have it instantly available anyway. The only thing stopping your phone from having terabytes of storage today is that it's currently expensive, and not much demand for it vs. the slight extra space it would take (512GB SD cards are a thing, but apart from size - though micro-SD versions are bound to follow soon - the cost makes them prohibitive for the next year or two).
We're very rapidly approaching the point where - while there may be value in having everything synced to the cloud for backup and universal accessibility - you'll be able to store all your data on media smaller than your thumbnail. Storage density appears to grow far faster than peoples storage needs at the moment.