What you’re describing is literally what it means for general relativity to reduce to Newtonian mechanics. You can literally derive Newton’s equations by applying calculus to general relativity. In fact, if you ever get a physics degree, you’ll have to learn how to do it.
I personally think that “all models are wrong” does nothing to stop people from simply thinking in terms of practical inevitabilities, when it’s actually extremely important to understand that figuring out what’s “actually going on” was never even the concern of science in the first place.