Everything you said is true. Tone policing shifts the burden off of the white person onto someone else to change things. I've had this discussion with family members. I try to do my small part by translating from critical race theory language into terms that don't provoke such reactionary responses from my family.

But I'm coming at it from the perspective of trying to win converts to your side. If you're trying to get police reform or any number of other changes, you have to get at a minimum a majority of people in the city/state/country to support that change. It may put more of a burden on a group that has been burdened for generations to have to argue in a way that doesn't alienate the white audience, but the goal is to change their minds. Catch phrases that unite one side force the other to unite against them when the issues are far more gray and the other side may be receptive to some of the ideas if they're presented in different ways.