I don’t think “black” “white” and “brown” can go away as descriptors like “blond” and “redhead”, but maybe someday they will stop being identity categories. America already has large non-native black populations in certain areas (West Africans, Somalis, West Indies, etc.), but I think the country still thinks of Black = African American = descendent of U.S. slaves for now, because the non-native blacks are still mostly focused regionally, like Somalis in Minnesota.
I guess this is another reason for the treadmill: distinctions that were implicit before maybe need to be made explicit as different things become salient.
Tl;dr your statement "The [euphemism] treadmill stops when you actually change public attitudes" actually means "The euphemism treadmill stops when you actually change public attitudes in such a way that I am personally comfortable with it's final state", because in reality the treadmill will never stop, someone will always push to keep it going, it's the reason why language shifts and changes over time.