Yup, logically it's hard to believe in walking dead period.
I mean, sure I suppose it's an irrational fear, but fear is still fear. If I could give you the series of nightmares I had that involved zombies, I think you'd be afraid too. One of the heaviest things in my dreams were the choices and the overwhelming ever-present despair and terror. It was strong enough I'd literally wake up suffocating from anxiety and too frightened to move.
Anyways some of that would also depend on the story. In some stories, animals can be turned as well. So other predators would only further the zombie apocalypse
However, I have read "zombie" comics and stories where it's zombie-like behavior in still living people. For example, in Black Gas, it was a black gas you breathed in that turned you into something like a zombie. It was some sort of neurotoxin that degraded parts of the brain turning people back to the most primitive of instincts. Cue lots of feeding, sex, and violence. Those zombies could still drive within the first few hours of the toxins setting in, but the neurotoxin would start spreading and come out through mucus, saliva blood, etc. and could be absorbed through the skin. If I recall correctly, it also worked on animals.