As was kind of observed upthread, the Borg have some similarities to zombies, and multiple zombie stories can be told without personalizing them.
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, becoming interested in assimilating people and turning them into Borg. In TNG this was a rare process; Picard/Locutus was the only person it was shown to happen to. But in First Contact
the zombie analogy was embraced wholeheartedly, with assimilation becoming a routine practice, and Voyager
followed that precedent.