Ah, right. I would guess that's because it's just a much more complicated theory, and is well-approximated by Newtonian gravity for weak fields, e.g. like in th

Ah, right. I would guess that's because it's just a much more complicated theory, and is well-approximated by Newtonian gravity for weak fields, e.g. like in the solar system. So applying GR to more everyday phenomena would just be a much more complicated way of saying almost the same thing. GR is written in the language of differential geometry, and before even beginning you need a good grasp of Newtonian gravity, special relativity, multivariable calculus, and ideally electromagnetism too, so it needs a fair bit of preparation. And in fact the methods of Newtonian mechanics aren't thrown away, but incorporated into the more general framework. In that sense Newtonian mechanics is a conceptual foundation for GR, so that's why it's still taught first at school