youtube can do this. kaltura has something, too. nice for kids and building joke videos or maybe for building your next presentation.
however, pro video files are BIG, and upload will take longer than actual editing process with usual upload rates.
More important: nobody wants to have a bloated webapp that runs in an already bloated web browser (all of them are!) and eats all your cpu power just by executing some cool javascript gui framework - you need every bit of performance for rendering.
Although video editing requires a level of performance that javascript is not equipped for, a web video editor is not a terrible idea.
I would imagine all the heavy lifting would need to be done by a plugin or a local media encoding server. Portability and a rich editing interface would be the key features. Collaboration and version control would be a nice feature too. I am surprised how terrible the top commercial video editing programs are at simply sharing a project file with another person. Video projects really need the cloud backing the source files and version control.
All of this can be done in native applications, but imagine being able to work on a video project from any modern browser. Maybe you don't even need a local media encoder, the server could render your changes and stream them as needed.
Edit: I would love to be able to edit video on my Macbook Air and have a GPU cluster in the cloud doing all my rendering.
I'm having trouble finding a source at the moment, but I believe that the BBC attempted this a few years ago. They eventually abandoned the project because as the editors needed the full resolution file of everything they were using to ensure the shot was in focus etc., storing them locally was a better option. I can't really see that changing in the future either.
An NLE that checked out files from a remote server and then made edits to a text based file from which anything could be shared would be very useful though.
