Is the FileAPI in HTML5 dead?

Question

Referring to the HTML5 FileAPI in particular.

I am going through the W3C specification proposals, and from what one can read here: http://www.w3.org/TR/file-system-api/<

Answer 1

The File API is distinct from the File API - Directories and System.

The File API itself is not only not dead, but reasonably well-supported. (IE8 being the only significant [and happily receding] desktop browser without support.)

The Directories and System document...

...defines an API to navigate file system hierarchies, and defines a means by which a user agent may expose sandboxed sections of a user's local filesystem to web applications. It builds on File API, which in turn built on File API: Writer, each adding a different kind of functionality.

Apparently there were issues with it and so that effort is being abandoned, probably in favor of doing something else.

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...I can't seem to grasp how can browsers implement a feature and then suddenly realise they no longer want to support it

You may find this thread interesting. Basically, only Chrome ever had it. Mozilla, Apple, and Microsoft (and others) didn't want to implement it. E.g., it's not that Google decided they they didn't want it anymore, but that they never convinced the other vendors it was worth implementing. A web standard only implemented by one vendor isn't a web standard. The final nail was announced here.