You've raised what I consider to be the elephant in the room, and you can see all the responses quick to tell you why can't do that> It simply doesn't fit with what most people consider acceptable, which is that one must be a user for everything internet related.
Most of us have at least ~5Mbps/ 2Mbps (up/down) connections at home that are always on with minimal latency. The gaming service OnLive shows that these connections are adequate for most people's needs. Home/ office connections will only get better, and I think the idea of running one's own server(s) for things like family and/ or small offices will make more sense than some 3rd party corporation's "cloud." PIM, email, IM, pictures, videos etc. simply don't need to be subject to the whims or TOS of a company or outside one's own control.
This is what I do currently, and it certainly is a kludge at the moment, but I believe it can be improved to the point of appliance-usage eventually.