Is it really right that it is not possible to restore a backup to a different domain than the one it was created on in enhance? For example, I want to restore a backup to old.domain.com instead of domain.com?
You can do it manually. Just login to the backup server, transfer the files and db to the hosting server. Use command line to unzip and restore the DB.
The only issue would be the mailboxes that cannot be renamed. You'll need to create the new mailboxes and migrate the emails.