As Russell pointed out, this only makes sense when the user has little computing power but high bandwidth. That may happen sometimes, but usually it will be the opposite.
Computing power is plentiful and cheap. When people are at their usual workplace, they most likely have abundant computing power. That's also when they probably have the best internet connection, but the local computing power still wins. And this is ignoring the serious issues of security, privacy, paying for a service, where the results will be stored, etc.
When off site, most people that know they will be taking pictures and intend to process them will have a laptop with them. Again, computing power is available but internet connectivity maybe less so. About the only scenario I can think of where this makes sense (again, ignoring security, privacy, etc), is if someone has only a smartphone or small tablet with them. But then you have a user interface problem. To do post processing right, you need to see the pictures at a reasonable resolution and preferably in a situation with controlled or at least known lighting.
I sometimes take pictures in remote places where I may not see another person all day. When I get back to the car in the evening where I can post process pictures from the day, most of the time there is no internet connection at all. When I do have it, it will be over a cell modem. Clearly, doing processing in the laptop is a necessity.
So far I've skipped over the issues of security, privacy, cost, and where and how my data will be stored, backed up, and archived. These are serious issues which alone would probably prevent me from using such a service even if uploading and downloading were instant (which is essentially what they are when locally processing). I don't want to only be able to processes photos when there is a internet connection, let alone a fast one. And no, I don't know what you'll really be doing with my pictures regardless of what you may claim. What happens when your enterprise goes bust? Will all the servers be suddenly shut down one day without warning? How will I get at my data? I expect you won't be doing this for free, so how much will this cost? It just doesn't make any sense, at least not to me.