Why was work on the Directories and System part of the File API discontinued? It’s still very much needed, especially for use cases like uploading a directory (as Kyle tweeted about).
https://lists.w3.org/Archives/Public/public-webapps/2012JulSep/0791.html says it “hasn’t been widely accepted nor implemented and also because there are other proposals which handle the same use cases.” (searching like “filesystem note site:lists.w3.org/Archives/Public/public-webapps/” might give you more details.)
Good news is one of the “other proposals which handle the same use cases” evolved and now is an official work item of the WebApps WG. You can take a look at it at http://w3c.github.io/filesystem-api/ .
Microsoft has recently published a proposed spec for directory upload: http://internetexplorer.github.io/directory-upload/proposal.html.