I never got around to trying it out. I think I may have tried to start some discussion on usenet along these lines maybe 10-15 years ago, but no one seemed interested.
A "directory" would simply by a process that provides some kind of lookup service to let other processes find the data storage processes that contain the data they are looking for.
You'd still have disks on your computer, but they would be mostly used as swap space.
The system would include some standard simple data holding and directory processes that implement a Unix-like namespace and permission system, but it would be easy to override this for data that needs special treatment. Just write a new data holding program that implements the special treatment you want and knows how to register with the standard directory processes.