So Andy, how did you test this and find that notifications are available only if "set moderator privileges" is set? Because I'm seeing otherwise.
From my Owner account, I removed 'Set Moderator Privileges' from my Mod account. I then logged in with my Mod account and the Moderator Notifications panel was no longer accessible/visible in the membership record. From my Owner account, I checked 'Set Moderator Privileges' again and the Moderator Notifications panel was then visible/accessible again from my Mod account membership record,