A file is an arbitrary string of bytes. Removing the ability for the user to handle them like this is so obtuse.
Per the article:
According to the BTRON3 specification, the first two halfwords of an application ID are the data type it applies to, and only the third distinguishes rival handlers for the same type. When a document contained writing, a table, and a figure, opening those parts made the system launch each one's registered handler to draw its own content inside the parent document's window. If no handler exists, or the handler fails to draw, the system strikes a diagonal line through the region where the content should have been.
That's a window manager with application/file associations, with the 'window' that the application draws to being embedded within a hypertext document. So, you'd be able to attach arbitrary hypertext to a file and when you open it the window manager presents that information along with the application window. That's not any less flexible or more limited than any other desktop OS.
EDIT: now, it sounds like you could embed multiple 'windows' within the same document, and maybe do something with transclusion, but I haven't read enough about how BTRON worked to say much about that. Still, that doesn't fundamentally change what I wrote above.
Every single mainstream operating system has metadata and index stores associated with its files and applications.
Linux has locatedb and .desktop files, and many other files that determine how content is presented to you in a desktop environment.
Windows has NTFS alternate data streams, the registry, multiple appdata folders, and a bunch of other kludges.