Distortion just changes the roughly sinusoidal output of a guitar to a square or triangle wave. These are the same waveforms created by reed instruments and bowed strings. The original fuzzboxes were incredibly harsh and primitive sounding but modern distortion devices are extremely musical and give the guitar a nice sustaining quality, allowing the player to play the same lines that a horn or strings player can play. You mentioned that a pipe organ can replicate the sounds of some other instruments. In principle this seems to be same thing that guitarists are doing with distortion.
Make no mistake like that other pompous guy on this thread, I know my taste in music is no longer main stream.
Funny you should mention reeds and their waveform as they are my least favorite pipes in the organ. They can (not all) have a buzz to them. A free reed clarinet is as smooth as velvet.
You are correct in that my ears prefer a rounded sinusoidal wave form so typical of many acoustic instruments.
Regarding Rock & Roll, it did exist before the electric guitar and I loved it. It lost me with heavy metal and the wailing of something akin to a tuned dentist drill and the obnoxious Wall of Sound.
Mediocrity has succeeded big time in so many fields of endeavor.
Popularity does not always equal high quality. EG: McDonalds, Microsoft, RAP...
Anyway enough thread drift. Cheers.