Newtonian physics is not "a hack". It yields very precise results for simple gravitational interactions, at least up to the point where relativistic effects begin to dominate. Even Einstein's equations are not 100% "perfect". All mathematical models have their limitations. (Although some do produce better approximations than others.)
A hack is in the eye of the beholder, and many hacks are load-bearing and totally fine for the entire timespan for which the thing they're stashed within is expected to be useful. I agree with you that all mathematical models have their limitations--but the choice to use a good-enough one is, over sufficient time and distance, a tradeoff that can be described as such.
