Graphics are actually a bit weird in this regard. A typical computer will take of the order of 100ms to go from user input to showing the user a screen of data. You go from Europe to the US and back in the same time period with a packet of network data.
The difference of course is the amount of data that is transmitted within that 100ms. Just the raw image itself is 6MB or more and the assets used to generate the picture are GBs in size and the world state is GBs as well. So its not like a server on the internet somewhere can work with any of these assets or the game world as sourced from the console, its simply too big a state to be transferred out from the game, to a server, processed and then returned back in any sensible time period. 3D Graphics is a data heavy process and you need very high bandwidths to do anything useful with it and latency in graphics is a big problem.
In theory at least the console could be used to offload completely and just decode a compressed stream using one of the existing services. Of course most players notice the additional latency, the compression and the low graphics settings but it does mean that a console today could show much better graphics if the game was run remotely but obviously with the drawback of latency and some loss in image quality. Maybe in the future when we all have fibre run into our homes it becomes a bit more viable in terms of graphics quality but it will still have a latency issue, an issue which will always mean that cloud computing can't be used for anything latency sensitive that the console itself is processing.
There is very little a cloud service can do to improve a consoles performance beyond taking over the job of rendering the game completely. The world data state is simply too large for todays internet connections and latencies, it most likely wont be solved within a decade.