You're assuming the database is tied to each application; that's only one possible approach.
NEPOMUK (currently a KDE project) is an example of a database which is independent of any particular application. It stores RDF metadata about each file (and about other things too, like contacts, events, etc) and provides a common ground for any application that connects to it.
In the end, the filesystem is just a key-value database too...
Yes and no. Google Desktop was a fully contained application; indexing was just an internal mechanism for its own functionality.
NEPOMUK is closer to an actual filesystem, in that it's not user facing; it's a service for other applications, like email clients, media players, etc. This allows them to almost effortlessly¹ share information like user contacts or music metadata.
¹ Apparently, a basic but functional email client can be built on top of the platform in 10 minutes.
NEPOMUK (currently a KDE project) is an example of a database which is independent of any particular application. It stores RDF metadata about each file (and about other things too, like contacts, events, etc) and provides a common ground for any application that connects to it.
In the end, the filesystem is just a key-value database too...