I frequently catch myself writing code more from the "I am able do this" rather than the "should I do this" point of view. In my experience, not having a clear goal that benefits a user makes it hard to get any idea adopted.
What do you think an empowered user would want to do? All the pieces are probably there to make things work.
But to try and give a more direct answer to your question: I often want to download/backup or otherwise programmatically process content that I routinely interact with online (this could be playlists, emails, messages, whatever). Another interesting example pertains to the “agents” available in “Huginn”: https://github.com/huginn/huginn
It would be nice if more such capabilities were integrated into the browser (or other common operating tools).
The semantic web hasn't been adopted, so one challenge would be how to categorize and expose the content to any sort of API. Perhaps such a system already exists.
The emacs ecosystem is a good example, but as you stated, it really requires expertise to utilize. I know of commercial service like IFTTT [1] but the thought of having this type of service be a utility available to any browser user is more interesting to me.