Wish there was a Web app to edit video. Upload to S3 and away I would go creating (jump cut) edits which would be fed to ffmpeg to dice up.
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.
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.
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.