Every time the administrator restores a backup, this always appears: Outgoing email has been disabled for non-staff users

This is intentional. I suppose, to prevent users to be spammed with unintended mails when restoring a backup to a staging site.

You have to change the config option disable emails by hand.

Except for updating a staged site, can one assume that the frequency of restores is rare?
For cases of automatic restores, such as when synchronizing a staging instance, these configuration values can also be set via a script.