Postfix and dbmail are different things. Postfix is an SMTP server (an MTA), dbmail, on the other hand, is an MDA and a set of daemons for accessing mail in its backing store. It's much closer to Cyrus or Courier than Postfix. This diagram might help:
http://dbmail.org/dokuwiki/doku.php?id=bigpicture
Some of the advantages to dbmail and its use of a proper database as a backing store are listed here:
http://dbmail.org/index.php?page=overview
Filesystems are finicky, performance varies wildly across workloads, they may or may not scale, remote access (e.g. NFS) has always had more than its fair share of issues, and filesystems are not built to make what we think of as transactions very easy (witness the recent confusion with ext4's completely-compliant but surprising-to-many-developers metadata behaviour).
A good RDBMS takes care of these issues and more for us. They're specifically built to handle large quantities of related data in a reliable, efficient, and scalable manner, and provide consistent, concurrent access to that data.
Another nice bonus: backups are trivial. Just mysqldump with the --single-transaction and --flush-logs flag and you have a snapshot that's guaranteed to be in a consistent state, and you can copy off mysql's binary logs for incrementals.
ETA: TLS/SSL does have to be run through stunnel, but stunnel is trivial to configure.