I have software deployed that depends on locally run (MySQL) DBs sitting on user/retail outlet machines, and I could think of a few reasons. Big data downloads, modifying anything about the data structure can cause breakage between the middleware and the DB, you're basically distributing a data model along with what should normally be serverside code to the client. Conceptually it's great but for large data, I'd hate to be paying for the bandwidth if it were public. And if it's not just a web page, you need a way to update it on every platform. Also, there are always things in a web app that simply cannot be client-side because they'd pose a security threat.

The concept reminds me a little bit of CD-ROM multimedia, in that it's so self-contained. For something like that it's great.