The benefits of hiding a file extension that I know of are user-friendly URLs, and a thin layer of security (I say thin because if someone really wanted to find out the extension of a file whose type has been hidden, it probably wouldn't be difficult. Am I wrong?).
But why should you do this (hide the extension), rather than use a file of type "file", with no extension? For example, if I have an extension-less file named "404", <a href="/path/to/404">Error page</a>
works without error (pretend I have absolutely no IE visitors).
Is there any added benefit of actively hiding the extension of a file that has one, over using files that don't have extensions? See any linked pages from schema.org for an example.