I am currently in the process of consolidating a few dynamic websites (wordpress-based) from different providers, and a very common workflow is 1) exporting DBs via phpMyAdmin, 2) SSH'ing into webmin or phpMyAdmin 3) uploading the downloaded data to the new server and 4) importing it - so, being able to directly tell webmin to SSH into another server via password/pubkey auth and tunnel mySQL/mysqldump over SSH could be a great time saver
I believe that this could also be a useful building block for the extended "migration" feature that we talked about in the other thread recently.
From a workflow standpoint, I am typically grepping htdocs for old DB credentials (user/password) and running sed in order to adjust files for the new credentials. Likewise, I am also grepping for the old htdocs path to track down any hard-coded paths and replace those, too.
Just my 2c obviously :-)