Definitely something we are looking into. Major barrier is the cost for someone keeping a server running 24*7 in cloud(Micro instance on AWS is 175 dollars a year).
Some of us already have servers running 24-7 in the cloud. I have two, for example.
What about using your server to run the software, but flat files as storage, I could point it to dropbox for example?
Lots of us here have our servers.... Personally, being able to point it at one of my own servers and/or getting an API, would be fantastic.