Zombies are the perfect mindless threat. I'm a fan of zombies in movies and video games and tabletop games. Do you want to know why? Well, there are 10 reasons.
You can kill them without remorse. You'll never walk into the back room of a bunker to find the innocent zombie women and children presenting you with a sudden awkward moral dilemma in the middle of your hereforeto heroic killing spree.
They pursue fresh brains to eat. That's all. When they need to be clever, they can be clever with plausible deniability that they've retained enough muscle memory to do some clever things because that's how you get more brains to eat.
They can have guts leaking from their rotting flesh, or they can just look like that one guy who never bathes.
Fantasy, modern, sci fi. Zombies work in any game.
Everybody knows a headshot kills a zombie without fail. But if you don't get the headshot, then that same weak zombie is as relentless as it needs to be. Chop a zombie into pieces, and what do you get? You get its zombie hand scurrying across the floor to deal further damage to you. Or the zombie explodes, spewing toxic bile on every ally within range.
Need more threat? Add more zombies.
The typical zombie is relatively weak. But recent research into zombies has revealed that there are inevitably a few boss-level zombies when you really need them, and lots of ranks in between. Modern zombie hordes feature shamblers, runners, ragers, spitters, exploders, crushers, bloated crushers, amalgamated mutant bosses, and more. (I think I made most of those classifications up on the spot, but it doesn't matter, you get the idea.)
Zombies are scary, and yet they can be as dimwitted and slow as you need them to be at the start of a game, when players are new and still developing their skills. As players level-up or the game starts to intensify, the zombies players encounter can get seriously dangerous.
Zombies have been a staple of horror for a long time, but I feel like in the 2010s they achieved pop culture ubiquity. The "zombie apocalypse" trope made its way into business plans, party games, more video games than ever before, and every genre of movie or book you can imagine. As a culture, we're all pretty much as comfortable with zombies as we are with super heroes. These are familiar concepts and a common language.
If you're a fan of the post-apocalyptic aesthetic, then zombies can fit nicely into it. It's superificial, but the look of zombies just happens to fit the motif I enjoy the most.
Of course, you don't need zombies in your post-apocalyptic setting. A world where actual thinking humans betray one another, even as the world falls apart around them, is an awfully effective theme. Your once trusted neighbour or partner trying to shank you for the last tin of beans is emotionally worse than a mindless horde of zombies trying to tear you apart. But when you don't want that kind of emotional weight in your game, you can always fall back on zombies.
I think most people consider zombies to be satire from the very first George Romero movie, but for me it was Day of the Dead that really establishes it. The movie features the undead roaming the Monroeville Mall, because that's what they would be doing in life. Most people take it as an overt statement about mindless consumerism and mundane modern daily life. Obviously you can expand this as much as you need for your game. Poking fun at mob mentality is an easy target, and you have the comment sections of all the best sites on the Internet to farm for inspiration.
And on the other side of the coin is the realisation that satire is based on reality. There's nothing more terrifying than someone you once trusted, admired, maybe even loved, turning against you with such vehemency that they can't be swayed by emotional or rational appeal. It's the stuff of nightmares, but in the zombie version, the person also wants to physically consume your brain.
Obviously you can emphasize this as much as or as little as you think necessary for the kind of game you're playing. When you need them to be, zombies can be as emotionally taxing as any real-world threat.