It seems to me that one of things this app might enforce is the idea that your work isn't really done until you've documented it and/or shared it. Pushing for measurement of using tools like Dropbox, Gmail, Basecamp, Google Drive, etc. might enforce this ethos. Yes, it's definitely not perfect: it's not tracking that time when you lean over and ask the designer next to you for feedback, and so on. But it seems worth an experimental try.
I know many very productive people who seem less productive than they are, because they hate going to some project management tool and documenting what they accomplished. If we could semi-automate documentation of work being done, such as by hooking in to Github, that might make their progress more visible with little to no effort.