[dontreact]

I believe you are are vastly oversimplifying this.

An impulse response will characterize only a system that is

* linear

* time-invariant

Many effects are not linear (especially distortion: the crunchiness comes from the nonlinearity). f(a) + f(b) != f(a+b)

And many effects are time varying, for example phasers and choruses which have low frequency oscillators controlling how the sound is shaped depending on when it comes in. Chorus for example will vary the pitch up and down.

[aerospace_guy]

Yup! This covers the basics of control theory; a simple concept that most don't understand.