To some extent, those sorts of motifs are a dramatization and personification of
death itself. A very real threat that's usually rather immaterial and conceptual, cast as something you can see and touch. And that can chase you down an alley.
Nothing got you today. But something might have! And something definitely will sooner or later. It's always lurking, it doesn't rest, it's relentless in its mission, and it can strike at any time. If it hasn't taken someone you love, just wait, it will—in fact, it'll take everyone you love, eventually, if you stick around long enough.
You see similar use of the unstoppable-killer with marked victims (achieved via copycats and other trickery in Scream, but it's the same idea) for the purpose of representing other fears, traumas, or threats that have a degree of universality and don't tend to entirely go away, as in It Follows. You see this whole thing made perhaps a bit too on-the-nose in works like Final Destination—which is why, I think, you can have endless unstoppable-knife-guy movies and they may retain some appeal, but a little bit of a "cute" very-literal twist on the formula like Final Destination goes a long way; the world only needs so much of that, much as a joke that subverts a particular standard joke-form only works once or twice before it stops being amusing.
The fun thing about the Scream series, when the movies remember it, is that the killer's emulating this fictional trope of an unstoppable and possibly-supernatural-but-not-omnipotent killer on purpose, in "real life", which is good fodder for creative narrative, twists, and well-earned winks at the camera. The movies are meta not because they've arbitrarily chosen to be (though they do choose to lean into it, of course) but because they aren't about these kinds of fictional unstoppable-personification-of-death killers directly, but about "real people" doing the unstoppable-personification-of-death thing in "real life", in imitation of film (even in the first one, before the idea of copycats hunting the survivors entered the picture, there's a particular thing done in order to imitate not just a human knife-wielding killer, but specifically this kind of wholly fictional, unkillable death-dealer).
Actually, as with Final Destination, this is another thing the world only needs so much of, for similar reasons—I'm not sure the market would support a much greater rate of release for this kind of film than we already see. It's not as immediately-played-out, though, less of a one trick pony.