I did a deep dive into this, but this just seems to be the case about sinusoids. technically any well behaved periodic functions can be the basis function for all fourier-related stuff (there actually is a FT where a square wave is the basis function, but I can't seem to find it) but there seems to be something special about sin(x) and cos(x) that makes it more convenient to analyze our physical world. They seem to be the result (and the only result) for some class of very simple linear differential equations, which because of its simplicity, happens very often in nature. That's why FT uses sin(x) and cos(x).