Your premise that "everything from moon to stars is local and predictable" is incorrect, both on the "local" (some celestial bodies are local, others are not) and "predictable" (what does that even mean in this context?)
I think we'd have to first understand each others position here. I assume the FE community would generally agree that the firmament is some finite distance above the earth and everything is locally contained. There are some FE people that don't hold that position though, and you may be one of them, which may drastically change the discussion. I could be wrong in my assumption as well. Regardless, if there is a firmament, then shooting stars and rocks from "space" would have to be local, or inside the dome.
Predictability: There are some objects like junk satellites, some space debris, and some rocks/comets that we can track. Halley's comet for example (since y'all mentioned it) comes around every 75 years and will return next in 2061. Whenever it returns, a part of its debris field becomes fireworks for the observers on earth. Meteor shower events happen relatively frequently where they are predicted and observed.
There are some things we can't track, and as aforementioned, we are trying to make space travel safer and also find earth-ending sized rocks that are close by.
I think maybe your critique of my post is you think I'm saying we can predict all or most the shooting stars on an average night. We can't do that. Most of what we see are no larger than a pebble or grain of sand, and we can't track that. We can track bigger ones, and those typically come with a debris field that gets sucked into our gravity.
However, there is a much bigger problem with your query. It is unclear why you think objects in space would have no component velocities other than downward relative to the Earth, and you did not explain why you think they would.
I'm confused why you're confused... I said "non-vertical". Objects do enter the atmosphere at a shallow angle, not perpendicular to the earth. Perpendicular entry doesn't happen as earth tends to yoink objects out of their own orbit as they travel somewhat parallel to earth, so they enter at a very shallow angle. My problem with the theories thrown around in this thread is that there wouldn't be a large lateral velocity associated with any of the possible debris that could fall from the sky in a flat earth model. I'm not sure if the following statement will be conceded (but I'd be delighted to discuss it): most of the shooting stars you see are moving somewhere around 80,000mph, and a negligible amount of that velocity is towards the earth. For reference of the magnitude of the speed, you would personally burst into flames if you ran at 3,800mph or mach 5.