It's true that Newtonian physics has not been discarded, but I think you're greatly underestimating the intellectual chasm that had to be crossed to get from it to relativity and quantum mechanics. The idea that not only velocity but also time, distance, and mass are relative; the wave/particle duality; the uncertainty principle; quantum entanglement; curvature of space-time -- all these were shocking, mind-bending ideas at the time they were first broached. They all seem to fit together neatly now, in retrospect, and we understand that Newtonian physics is a useful approximation that is quite sufficiently accurate in a lot of everyday situations, but the way we think about physics now is almost inconceivably different from the way we thought about it 200 years ago.