You could still calculate that with an earth-centric approach, it just might not be fun. As far as the physics go, it doesn't care which point or body you pick

You could still calculate that with an earth-centric approach, it just might not be fun. As far as the physics go, it doesn't care which point or body you pick to be non-moving - the math all works out, it's just relative to a different point. And with that, there's no spot in the universe you can point at and say "That point is not moving", so there's no "fundamental zero" we can compare everything to. Perhaps the point is that "more correct" is subjective. Both approaches will give you the right answer, it's just that heliocentric makes finding the answer easier.