The primary reason this is Chrome-only is because other browsers don't yet have complete implementations of relevant specs (for example the FileSystem API: http://dev.w3.org/2009/dap/file-system/pub/FileSystem/). I can't make any promises on the team's behalf, but I personally would like to see it working on Firefox as well at some point.
I'm curious what y'all are using the FileSystem API for and how you're using it. If you wouldn't mind talking about that (or have other people on your team that would be interested in talking about it), drop me an email at <my-hackernews-username>@mozilla.com.
It looks like they're leaving out everything in the spec I linked above. Currently this is the only way to persist File objects locally, although it looks like they're planning to make that possible through IndexedDB instead.