They exist! The crystal structures of molecules are rather Platonic, for example. Nature is elegant when you get very small, requiring fewer and fewer core concepts as you work your way down to more fundamental levels of understanding. (At lower levels those fundamentals might be irrational ones, but still, those few primitives [like spirals in complex space] become the only tools you need.)

The inelegance, then, comes from modelling the interactions of mind-bogglingly huge collections of these fundamental things, at high levels of abstractions, and then expecting your abstraction (which is just that: a formula that allows you to make some useful prediction of these super-high-level interactions) to be as elegant as the fundamental forces operating at the lowest levels.