> Newtonian mechanics is extremely simple, yet it is only true as a limiting case of relativistic mechanics, which is not as simple.

On the contrary, relativistic mechanics is strictly simpler than Newtonian mechanics, because the symmetry group is enlarged by the inclusion of time on equal footing with space. A few extra squares/roots don’t make relativistic mechanics less simple than Newtonian mechanics. I cannot emphasize this technical point enough — it is extremely important. More symmetry means fewer parameters that need to be empirically fitted to data (or hand tuned), which means more predictive theories.

This is why symmetries are placed on a pedestal in fundamental physics, and taken as the organizing principle, as far as we know.