Managing Household Responsibilities -
I began as a young father in 1972 with "household responsibilities" and am now with my wife of many decades, having had 4 kids, who have had 6 grandkids. All this to say that assigning tasks is not like an efficiency expert, or a teutonic agenda set in stone.
You start early. In the 1980's I was at home with my fourth child - a stay at home Dad for two and a half years. Part of the "assigning" is engendering a spirit of picking up as a part of family hood. My little one was encouraged to pick up after herself. Now this is not a miracle. It is just a natural urgent message that part of playing is to pick up after the playing.
Part of cleaning tasks is to just rotate the assignments that are not liked. Then the kids can trade days, exchange the chores like currency. Their are easier tasks and ones that are age related or gender related. They can be assigned this way.
Of course, this is noisy and seems to be arbitrary. When there is noncompliance, punishment by the parents can be "nonviolent" by extending duties.
The more joyful and high speed this becomes, the better. Boys get garbage. And girls get dishes. This is kind of a traditional way of dividing. However, if the kids can change duties back and forth, the parent should not mind, as long as it gets done. If it does not get done, and the remedy does not seem to take effect, then the parent should examine if someone is getting too much work or not enough work.
If there is a general revolution or juvenile upset, then the family should sit down and reformulate the answer.