I don't think you know what you are talking about, Olivier. I don't know if you are trolling me... or if this is some sort of weird one-upmanship.
Early in any Physics class you run into the issue of of precision (as opposed to accuracy). You need to understand the difference in order to get the issue you are raising; that is, classical physics versus relativity. Newton's Laws highly accurate in all but extreme circumstances. You trust Newton's Laws every time you get onto an airplane or drive in a car. They got us to the Moon and to Mars.
Physics students, when they start to cover relativity, generally go through the exercise of calculating the difference between calculations using classical Physics (i.e. Newton) and Relativity. The point of this exercise is to give students an understanding of how accurate Newton is in almost every situation (outside of the extreme examples).
I don't know if you have every studied relativity and gone through this exercise (or if you are just googling exceptions to score points). If you did, I don't think you would use the phrase "good enough approximation".
There are correct answers in Science. And when you are talking about the motion of cars, airplanes, any existing spaceship, robots, birds, engines, motors, bullets, missiles, baseballs or flying fish.... Newton's laws will get you the correct answer.