You can do a lot of laundry in a shorter amount of time with a wringer and rinse tubs, but the brief scenarios given here do not hold up through a whole family wash. One person cannot run at that pace for long. In wringer washer situations I have seen, there was at least one child helping. The physical energy involved in the rinsing and wringing, the carrying the clothes, usually upstairs and outside, the hanging of heavy wet laundry on the line in the heat of summer and the windy cold of winter when you had to stop and bundle up and clothes freeze-dried on the line was brutal. So the pace slowed and had to when you considered the progressively more heavily soiled items, cooling wash water, having to change the rinse water, etc. And like Kelly said, many families had to heat the wash water on the stove, in my paternal grandmother's case a kerosene one in the basement with 3 burners lit under the boiler. When the water boiled, it was dipped out with a pail until it reached a low enough level that my grandmother would have her husband or my mom, when we were visiting, help her hoist it by the handles and pour it into the washer. That was dangerous as well as strenuous. By that time, they lived in the city so at least a hose from a faucet was used to fill the boiler and the rinse tubs. Since her husband was a cheap bastard, her rinse tubs were 3 galvanized tubs on an L shaped platform and at the end of wash day, they either had to be bailed out partways with a pail or tipped gradually to empty into the floor drain. That wet floor sure helped keep the basement humid, even with the Dorothy Gale storm doors open so that laundry could be carried out to the lines. Of course in Iowa winters, you could not use the doors, so if laundry was put on the lines outside, it had to be carried up the narrow steps, through the dining room and out through the kitchen door, if there was not too much snow. Otherwise, lines were strung all over the basement which was not large. I guess for just the two of them, it was not so much of a problem. One of the reasons that mom gave for not needing a dryer was that she had a basement in which to hang clothes in bad weather. I remember that we could not roller skate in the basement if she had laundry hanging down there and if it was rainy and cold like so many winter days in Georgia are, bad weather for skating outside was bad weather for drying outside.
And food. Laundry was not begun until the breakfast dishes and pans were washed. Lunch was something like sandwiches while watching the weather and checking for birds. I remember the look on their faces when 2 freshly laundered sheets had been hit with purple berry bird poop after all of the laundry had been done and all of the equipment was rinsed out and dried.
In surveys of women in this country, they always ranked the washing machine as the most important labor saving invention. I would bet that the electric wringer washer was as big or bigger a step in saving time and labor as the automatic was when it was introduced later for the person doing laundry. It's also why so many of the Bendix Home Laundry automatics sold when they were the only automatic, even though they did not wash as well as a good wringer washer.