Do note that profile #1 is the default backup profile and cannot be removed, as noted in the documentation. We need a default backup profile so that when you ask Akeeba Backup to load a backup profile which does not exist it can fall back to a well-known backup profile. Because of when this need may arise, e.g. in a CLI script before the database driver is available, the backup profile ID can neither be stored in the database, nor the component parameters (which are also stored in the database). It would have to be either stored in a file (which causes all sorts of security, performance, and reliability issues) or it has to be hard-coded. It is therefore hard-coded to #1, which is why that profile can never be deleted.
Also keep in mind that there is no such thing as “unpublishing” a backup profile either. If you pay closer attention to the Profiles Management page you will see that this column is called One-Click Backup Icon, not Published. It only controls whether you will see an one-click backup icon in the main page.
According to your log file there is a CLI CRON job or Joomla! Scheduled Task being triggered by a CLI CRON job which is trying to use profile #4. Since profile #4 does not exist, Akeeba Backup loads the default profile #1. The solution to your problem is, therefore, changing your CRON job or scheduled task to use a different backup profile, one which does exist.
Nicholas K. Dionysopoulos
Lead Developer and Director
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