Commercial Laundry Products
In addition to containing some very powerful and nasty chemicals such as sodium hydroxide (lye), oxalic acid, and so forth also are dosed in minute amounts per pound of washing.
It is not uncommon to see titration levels of 2-4 ounces per 100lbs of washing. Average domestic washer holds only 11-18 pounds of washing; so just run the sums...
As already mentioned nearly all these chemicals come with warnings against use in "home style" washing machines. There are products designed to work in institutional, OPL and other laundries with normally smaller capacity washing machines, but they are labeled as such. Also as per above post these chemicals will do a number on pumps, seals and perhaps other parts of a domestic washing machine.
Most commercial washers do not have pumps, but simply drain valves. Where there are pumps (such as for soft mount machines) one would assume they are built to a different standard than domestic washers.
Other issue with domestic washers versus commercial is the often total lack of programming controls. Many of these chemicals (oxalic acid is one) not only require hot water cycle, but several rinses in hot or very water to remove.
Now back on topic:
As have mentioned before soap even when used in water softened with precipitating
water softeners such as TSP or sodium metasilicate, and a wringer isn't bad as many would think.
This is because unlike automatic top loading washing machines that drain water down through the wash, when using a mangle/wringer (hand or power operated) one lifts laundry out of the mucky water. The mangle or wringer will then squeeze dirt, soils, soaps, etc... and most importantly hard water minerals and scum out of the wash and down back into the tub.