[meatmanek]

Frequency domain also makes the math really easy for linear, time-invariant operations, which (approximately) describe a lot of systems that exist in nature.

The Gibbs phenomenon, for example, falls out naturally from the IFT of a frequency response where all the frequencies above some cutoff are zero.

I'm curious how the square wave frequency domain would describe the Gibbs phenomenon -- I think you'd have harmonics of the fundamental square frequency showing up as if the system were nonlinear.