Except zombie stories do have a personal stake, because zombies are specifically going after people, and because they can be the corpses of people who used to matter to the characters. The Borg as originally defined in "Q Who" had no interest in people, only technology, and their drones were grown in incubation vats, not assimilated. In order to give subsequent Borg stories more of a personal stake, the Borg were changed to be more zombie-like than they had originally been,
True, but that didn't
necessitate the Queen, so no, zombie-type villains do not need to be given a 'face' to continue to work in stories.
(A vaguely related argument would be whether or not assimilation was necessary either - in some senses, the Queen is the natural response to the assumption the Borg enslave new minds, rather than have them birthed. An ant-like society of hive mind drones may not have individuality, but they may not be slaves, either - since the decisions of the whole would come organically from that collective, a transhuman one-brain one-vote system... or not.)