TYPO3 Core

Since features like "random subpage" won't work on files (or content-elements) imho we could simply create a new type of shortcut (in the type-dropdown) and add those two cases there. The shortcut would then instead of a page-id point to a "file-id" (FAL) or a content-ID (tt_content).
We'll need to have matching popups to select the content then. (Those functions are already there.)

Linking to content-elements is somewhat related to #17037, where in the end due to workspaces etc. the linking to content-elements was skipped. But it sounds doable to me - not?

This can be realize by this extension http://typo3.org/extensions/repository/view/ts_page_file_shortcut
even on TYPO3 6.1, but without FAL support,
btw it would be nice to have this feature in the core.

There is also https://typo3.org/extensions/repository/view/filepage alas, compatible with 6.2 only

Isn't this possible now with the link handling?

As far as I can see, currently you can't add tabs (using linkhandler) to the popup that lets you select a destination page for the shortcuts.