Language is power and can greatly influence and define what masses of people think about their world view and their experience. Those who get to define which language is "appropriate" and which is not have a certain power to take as they please. "Tone-policing", "cancel culture", and "identity politics" aren't unique in the sense that they are designed to seize power, as this is a tale as old as time. It's a strategy that proponents believe will help their in-group and followers acquire and maintain power over cultural resources.
I'm not saying this example is good, bad, or neutral - just what it is: Using language to project influence and power and take the cultural resources you want.