Ok. Audibility. Linear operations do not add new frequencies. You can change timbre, tonal balance, etc, with linear operations, but you don't create new frequencies.
Your ear is a frequency analyzer. It is relatively insensitive to small changes in tonal balance, compared to having new frequencies added to a signal.
Nonlinear distortions DO add new frequencies. If these are small enough, no harm, but when "new frequencies" rise above the masking threshold for a signal, most often this is bad, bad news, unless you're creating a sound, say, by overloading a guitar amp on purpose. One of the gotcha things that nonlinear operations do is create sum and difference frequencies, and therein lies the disaster, say, if you create new frequencies in a part of the audio spectrum where there is no energy. The usual result is "ech" if done without intent, at least.
I'm not addressing artistic modifications to an original. For that, use whatever you want.