It has already been built. Bane's point is that why doesn't dropbox buy THOSE services and see if they can expand on it. For example docker.io is a paid service for the above use case. Dropbox might be getting a cut from them, but if docker has successfully demonstrated that there is a market for this, wouldn't it be better form dropbox to aquire them and push in that direction?
OwnCloud's plugin architecture allows for all of these things mentioned. But plugin authoring for OwnCloud is opaque and tedious. There's a Hello World and a few examples, but the environment isn't fun to work around.
I actually think DB should be the webserver in this case.
Why can't I just make a "web-server" folder in my dropbox, drop a bunch of html, js and css and a few image files in there, get a URL and voila, instant website?
You sorta can already in truth, but they don't like it and the bandwidth is pretty severely capped on these kinds of sites. Make it part of the paid account (with x-fer up to 1GB/mo or whatever) and have high bandwidth users pay more?