Hello, thank you for the suggestion.
Here are a few difficulties encountered:
a) application does not interact with the database directly - it does the backup by asking the forum admin interface to do it, which in turn, asks the database. It means there's no API in the application which directly communicates with the database. Hence, no API to ask the database to restore a backup.
b) connecting to MySQL directly would be an error prone process - since it would mean to have a script on the forum which mediates between the application (still connecting online - since many users don't have control over their shared hosting DB). Then it means securing it, passwords, ability to rename it to whatever the user wants (a bit of obscurity, if you want, not to have a standard name). Also, the script would have to be separate from the forum, as it should also work when forum is down and being restored. A whole new application. Retrying if upload fails (dropped connections), etc.
c) Limits: any web server has its limits in regards to file transfer. Users would have to reconfigure their server, timeouts probably, etc, and many shared users don't have access to these kind of settings.
As you can see, it would take a lot of effort to just create a feature that normal users maybe would never use (and if you really need to restore one backup, you can easily do it with phpmyadmin) - or upload it via SSH and execute the reload from command line.
Thank you for your understanding,