Scientific Soapmaking is a good book and worth a read, but some of the things I'm talking about here come from modern soap making technology books as well as scientific papers and books. I don't know of any one reference that has it all, especially in primer form. Dunn tries to digest this heavy info and present it in a simpler, more understandable form to handcrafted soap makers, but even his book and presentations require care and attention from the audience.
"... And with certain fatty acids stripping oils and proteins from the skin, I have to admit I thought all types of soap did that..."
Not necessarily. There are shades of gray here, but I'll give an analogy to explain.
Have you ever accidentally smeared a finely powdered soap colorant on your skin -- maybe a bit of ultramarine pigment or mica -- and tried to quickly brush it off? It really sticks to the skin, doesn't it? Now think about rubbing your skin with fine sand. It would brush off fairly easily, perhaps leaving a bit of dust behind, but not much residue.
Soaps made from myristic acid and shorter fatty acids are more like the powdered colorant. Because of their small size, they are able to "stick" more easily to the proteins and fats of the stratum corneum and pull them away from the skin.
Soaps made from lauric and longer fatty acids are more like the sand, especially the longer fatty acids (palmitic, stearic, oleic, etc.) They don't chemically bond as well to the surface of the skin. They still emulsify fats and loosen soil, yes, but due to their increasingly larger size, they are not as able to stick onto fats and proteins attached to the skin and remove them.
It's important to distinguish between cleaning and irritancy. Your skin can be clean but not irritated. Or your skin can be clean but also irritated. The choice of fatty acids can make a soap less irritating or more irritating, especially for people whose skin is particularly sensitive to that kind of thing. But even folks with fairly normal not-so-sensitive skin can react to an irritating cleanser by becoming taut, dry, and flaky much quicker than if a less irritating cleanser is used.