Proper procedure for migrating a MySQL database to another Debian machine?
That is a normal procedure for setting up a new server from old database, so there's nothing wrong with this. Probably the reason there is no mention of the passwords getting overwritten is admins know the old passwords so can easily update them on the new server.

One thing you can do is modify the dumpfile to use the new passwords for root and your Debian admin user prior to loading it into the new server.