>>45
Those "over complicated methods" exist because they work. Transistors, lasers, MRI, solar panels, electron microscopes etc... try designing any of those without knowledge of modern physics!
Feynman has a few examples of "everyday" phenomenon in the book I mention. The one that I remember most is the diffraction grating. It cannot be explained without quantum mechanics, and microscopic diffraction-grating-like structures are responsible for the reflective properties of many everyday objects. Loads of stuff about glass and lenses, too.
Relativity is not as obviously useful as other things - it is an important correction to Newtonian mechanics that is essential for getting the right numbers in some cases. Although pime taradoxes are fun too.
You worry about real life situations being too complex to model mathematically because of many interactions happening simultaneously. In that case I recommend you study thermodynamics, where you learn to build up sophisticated statistical models from basic Newtonian mechanics. If you are instead complaining that physicists tend to disregard realistic factors sometimes to narrow the discussion... well, if they didn't do that nothing could get figured out! Fields of engineering are spawned out of advancements in physics, and in those fields people can concern themselves with how to make the models most practically useful. Physicists are mostly only concerned that they are correct.