> At low speeds relative to the speed of light, they have the same accuracy don't they?

When measuring signal (ie radio, light, gravity) from slow speed perspectives, newtonian physics is not as accurate - https://futurism.com/newtonian-physics-vs-special-realtivity - Eg we actually need to account for it between gps sattelites and we do so from the perspective of GR as well as the recent evidence of gravity propogation being restricted to localization (ie roughly the speed of light)