You are right. The use of chemicals to break the water and the high temperatures used for at least preliminary after rinses would not have led to soap film buildup on machine parts or laundry. They had such an alkaline thing going in the washers that they had to neutralize it with sour at the end. If Maytag users had used STPP in the wash and then stood around to add it to the first rinse, then reset the machine for another rinse, soap might have given good results but, not only is that not automatic laundering, they also did not have the training of commercial laundry personnel or the mandatory dosing formulas that caused those big machines to stop and buzz loudly when the addition of specified chemicals was called for. Later, that would be automated, but it is easy to understand why Maytag made that pronouncement about not using soap; the rinsing was barely adequate, some would say inadequate, for detergent.