The analogy is more like an easier to implement version of a system(Custom Frontend Data Store) is worse than the standardized system (Database) rather than one system(database) being implemented on top of another system(filesystem).
The database has more features relative to filesystem, so we wouldn't miss the filesystem whereas a powerful indexing system is a feature in database missing in frontend data stores.
Some other examples below(Firefox plugins which are file browsers, FTP clients, C programs informally implementing subset of Common LISP features).