Java Database Connectivity (JDBC)

Dear Sirs,
Maybe this will sound a bit strange, but it is probably a good idea:

In a three layered tier application the client receives the presentation code from the middleware layer, so theoretically speaking layer 0 is obtanied from layer 1. Wouldn't it be a good idea if layer 1 (middleware) obtained the database driver directly from the database layer (layer 2)? That would avoid the intall of the driver class files in the server and would be coherent with the way the first two layers work together.

Thanks in advance fro your point of view.
Best Regards,
Ramon Talavera