And you obviously do not understand digital signal processing. A number has meaning, distortion does not. That number represents amplitude, nothing else. When you change that number you change amplitude in a specific way. Distortion in meaningless. DSP changes the numbers in specified patterns to achieve a specific result. Can you change the numbers to replicate distortion? I'm not sure although I do not see why not. A number can not be distorted, it can only be changed.
Analog? It is essential only because that is what our ears understand. The only components that should operate in analog are speakers and perhaps amplifiers. Everything else is way better off operating in digital. Good examples are broadcast radio and the cell phone. Compare Sirius radio to standard radio, old analog cell vs what we have now. People who think analog signal processing is better are stuck at about 1981. As you yourself have just described, you can go almost anywhere with DSP and not necessarily in good ways. That is up to the programmer.